International
Tables for
Crystallography
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.7, pp. 156-173
https://doi.org/10.1107/97809553602060000942

Chapter 2.7. High-pressure devices

A. Katrusiaka*

aFaculty of Chemistry, Adam Mickiewicz University, Poznań, Poland
Correspondence e-mail: katran@amu.edu.pl

Nowadays, high pressure is a routine variable for powder and single-crystal diffraction experiments. By combining high pressure with variable-temperature attachments, one can reproduce in the laboratory the conditions inside planets and use them to study geological, biological and physical phenomena or for making new materials. In many X-ray, neutron and spectroscopic laboratories throughout the world, the diamond-anvil cell and other high-pressure devices are common. Their development has progressed dynamically in recent decades and this chapter outlines their history, the main types of devices and details of their operation, their advantages and limitations, their installation at large synchrotron and neutron facilities, and the latest achievements in static and dynamic high-pressure generation. Modern equipment can combine powder and single-crystal diffractometry with spectroscopic, dielectric, magnetic and other measurements on samples of various kinds compressed, cooled or heated to unprecedented magnitudes. The results obtained provide a broad perspective for understanding both fundamental physics and complex processes in living tissue.

2.7.1. Introduction

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Although life in the biosphere of Earth exists within narrow limits of temperature and pressure, these thermodynamic conditions are unusual on Earth and in the Universe. Most of the matter in the Universe is contained in black holes, stars and planets, where it is exposed to extreme temperature and pressure. On the other hand, interstellar space constitutes most of the Universe's volume, where both pressure and temperature are close to their absolute-zero values. On Earth's surface at sea level, atmospheric pressure is about 1000 hPa [1 atm = kG cm−2 = 9.807 × 104 Pa ≃ 0.1 MPa; currently, the pascal (abbreviated Pa) is the generally accepted pressure unit recommended by the International System of Units]. Under water on Earth, the pressure increases by 0.1 MPa for every 10 m depth, and rises to 120 MPa at the bottom of the Mariana Trench, 11 km below the sea's surface. A relatively low pressure change, to about 0.3 MPa at a depth of 20 m, affects the dissolution of nitrogen in human blood and can lead to decompression sickness (caisson disease); at 300 m in the oceans (3 MPa) and 288 K, methane forms stable hydrates, which constitute the most abundant deposits of carbon on Earth. All geological deposits are exposed to some pressure; at a depth of 1000 m this is about 300 MPa. Consequently, the structure and properties of very many minerals, formed and deposited in the crust, can transform considerably after their exposure to the surface. The syntheses of numerous minerals require high-pressure conditions. Thus, high-pressure experiments can provide indispensable information about the geological and stellar mechanisms, transformations and properties governing the matter forms, properties and distribution inside stars and planets.

Therefore, the pressure dependence of crystal structures is of primary interest to geologists, planetologists and astrophysicists (Hazen, 1999[link]; Merlini et al., 2012[link]). The most cited examples of the effects of extreme conditions are thermonuclear synthesis, the formation of diamond (the dielectric carbon allotrope), the formation of stishovite (the dense form of SiO2) and the propagation of seismic waves through the Earth's crust. The understanding of these and other phenomena requires that extreme conditions be reproduced and crystal structures investigated in laboratories. Most importantly, the conditions that are ubiquitous across the Universe are viewed as extreme only from our perspective of a narrow thermodynamic space, of a few tens of kelvin and a few megapascals around the triple point of water. From this narrow thermodynamic space, most of our knowledge of materials science has been developed. Extreme conditions allow theories to be verified and developed to a more general level. Moreover, extreme conditions can be utilized to produce new materials with desired properties (Hanfland et al., 2011[link]; Senyshyn et al., 2009[link]), including diamond or its other super-hard substitutes, or new forms of pharmaceutical drugs (Boldyreva, 2010[link]; Boldyreva et al., 2002[link], 2006[link]; Fabbiani, 2010[link]; Fabbiani & Pulham, 2006[link]; Fabbiani et al., 2004[link], 2005[link], 2009[link]). The key element for such research is a sample-environment device for generating high pressure in the laboratory.

The pressure at the centre of Earth is about 364 GPa, one order of magnitude higher again inside the giant planets Jupiter and Saturn, and over 1 000 000 GPa (i.e. 1000 TPa) inside small stars like the Sun. Structural determinations under varied thermo­dynamic conditions are essential for the general understanding of physical and chemical phenomena, and to gain knowledge about the properties of materials and to describe the world around us. Indeed, the biosphere where we live is confined to a range from 0.33 atm (0.033 MPa) at the top of Chomolungma (Mt Everest), 8848 m above sea level, to about 1200 atm (120 MPa). The most commonly discussed and studied thermodynamic parameters are temperature (T), pressure (P) and composition (X). In principle, they affect the structure of matter differently. For example, the primary change induced by temperature is in the energy of atomic, molecular and lattice vibrations, whereas increasing pressure always reduces the volume. These changes are interdependent, and the compression of a structure can also reduce its thermal vibrations, change the types of cohesion forces and reverse the balance between competing compounds of different composition. This concerns all compounds, not only minerals deep under the Earth's surface. An exciting example of a molecular compound undergoing such transformations is water, transforming between at least ten polymorphic structures at high pressure, and also forming hydrates, depending on the thermodynamic conditions. Hence, pressure is now utilized to generate new polymorphs and solvates that cannot be obtained under normal conditions (Patyk et al., 2012[link]; Tomkowiak et al., 2013[link]; Fabbiani, 2010[link]; Boldyreva, 2010[link]).

For these reasons, high-pressure techniques have been developed dynamically, and the breakthrough invention of the diamond-anvil cell and its development in the second half of the 20th century greatly intensified high-pressure research. Today, the effects of high pressure on various materials and their reactions are studied both in small laboratories in universities and at large facilities, which provide powerful beams of X-rays from synchrotrons and beams of neutrons from reactors and spallation targets. The large facilities are either international initiatives, like the European Synchrotron Radiation Facility (ESRF) and Institute Laue–Langevin (ILL) in Grenoble, France, or national ones, like the Diamond Light Source and ISIS at the Rutherford Appleton Laboratory in Oxfordshire, UK, the Deutsches Elektronen Synchrotron (DESY) in Hamburg, Germany, the Photon Factory in Tsukuba, SPring-8 (Super Photon ring – 8 GeV) in Hyōgo Prefecture and the Japan Proton Accelerator Research Complex (J-PARC) in Tokal near Tokyo, Japan, the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory, USA, the Advanced Photon Source (APS) at Argonne National Laboratory and Los Alamos National Laboratory (LANL), New Mexico, USA, the Lawrence Livermore National Laboratory, California, USA, the Joint Institute for Nuclear Research (JINR) in Dubna, Russian Federation, the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory, USA, and others. They provide access to the beams and high-pressure equipment to the general scientific community.

2.7.2. Historical perspective

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The earliest concepts of pressure are often associated with Evangelista Torricelli's famous statement `Noi viviamo sommersi nel fondo d'un pelago d'aria' (`We live submerged at the bottom of an ocean of air') in 1643, Otto von Guericke's experiment pitting the force of six horses against atmospheric pressure acting to squeeze together two hemispheres evacuated using the vacuum pump he had constructed in Magdeburg in 1654, and Blaise Pascal's measurements of pressure differences at different altitudes and his demonstrations of barrels being blown up by the force of water poured in through a tall pipe. The subsequently developed high-pressure devices were mainly of the piston-and-cylinder type.

At the beginning of the 19th century, pressures of about 400 MPa could be obtained, and at the beginning of the 20th century, often referred to as the end of the pre-Bridgman era, pressures up to about 2 GPa could be achieved. Then Percy W. Bridgman's remarkable inventions extended the pressure range greatly, to over 10 GPa (Bridgman, 1964[link]). He devised new techniques for sealing pressure chambers, developed the opposed-anvils apparatus and introduced methods for the controlled measurement of various phenomena. Moreover, he used his new methods to describe a vast number of observations and properties of matter at high-pressure ranges hitherto unexplored. Bridgman's ingenious designs of high-pressure devices, such as the opposed-anvils apparatus, paved the path for future researchers. His scientific achievements won him the Nobel Prize in Physics in 1946.

The Bridgman era in high-pressure research ended in the late 1950s, when the diamond-anvil cell, often abbreviated to DAC, was invented (Weir et al., 1959[link]; Jamieson et al., 1959[link]; Piermarini, 2001[link]). Soon after, the DAC became the main tool of high-pressure researchers; it gradually increased the range of attainable pressure by more than an order of magnitude, and under laboratory conditions it surpassed the pressure level at the centre of the Earth. Most importantly, the DAC allowed many new measuring techniques, particularly X-ray diffraction and optical spectroscopy, to be utilized. Before that, spectroscopic studies were limited to about 0.5 GPa. High-pressure X-ray diffraction, pioneered by Cohen (1933[link]) in Berkeley for powders and by Vereshchagin et al. (1958[link]) in Moscow for a single crystal of halite at 0.4 GPa in a beryllium high-pressure vessel, had been expensive, inefficient and inaccurate.

The DAC has become commonly available because of its low cost and easy operation. Today, the DAC continues to be the main and most versatile piece of laboratory pressure equipment and a record-breaking high-pressure apparatus. However, other sample environments provide complementary means of structural studies. For example, the large-volume press can be advantageous for neutron diffraction studies and in experiments where very stable high-pressure/high-temperature conditions are required. Naturally, the success of many high-pressure methods would not be possible without the development of other sciences and technologies, including computers, powerful sources of X-rays and neutrons and their detectors, and lasers.

2.7.3. Main types of high-pressure environments

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High-pressure methods can be classified as dynamic or static. In the traditional dynamic methods, the pressure is generated for microseconds, usually at an explosion epicentre or at targets where ultra-fast bullets or gas guns are fired at the sample. The explosions are carried out either in special chambers or in bores underground (Batsanov, 2004[link]; Ahrens, 1980[link], 1987[link]; Keller et al., 2012[link]).

Even shorter, of a few nanoseconds' duration, the shock compression generated in targets using laser drivers coupled to the powerful X-ray pulses of a free-electron laser, or an otherwise generated X-ray beam, can further extend the attainable pressure limits. While this laser shock generates both high pressure and high temperature in the sample (the so-called Hugoniot compression path), in the ramp compression, also termed the off-Hugoniot path, the signal of the designed profile from an optical laser affords terapascal compression and approximates iso­thermal conditions (Wicks et al., 2018[link]; Smith et al., 2014[link]; Wang et al., 2016[link]).

The advantage of the gas and laser shock-wave and ramp-compression methods is that the attainable pressure is not limited by the tensile strength of the pressure chamber. Disadvantages include the inhomogeneous pressure, difficulties in controlling the temperature, the requirement for very fast analytical methods and the very high cost. The kinetic products generated during the explosion and in the shock waves can be different from the products recovered after the explosion, and different again from those formed under stable conditions. In most cases the laser-generated shock annihilates the sample.

Static methods are at present more suitable for crystallographic studies. The first variable-temperature sample-environment devices for structural studies of liquids and solids were designed soon after the inception of X-ray diffraction analysis. Structural investigations at high and low temperature at ambient pressure were mainly performed either by blowing a stream of heated or cooled gas onto a small sample (Abrahams et al., 1950[link]) or by placing the sample inside an oven or a cryostat. At present, a variety of attachments for temperature control are commercially available as standard equipment for X-ray and neutron diffractometers. Open-flow coolers using gaseous nitrogen and helium are capable of maintaining temperatures of about 90 K and a few kelvin, respectively, for days and weeks. They are easy to operate and pose no difficulties for centring the sample crystal, because the crystal is mounted, as in routine experiments, on a goniometer head with adjustable xyz translations and is visible at all positions through a microscope attached to the diffractometer. Cryostats and furnaces obscure the visibility of the sample and are usually heavy, and hence require strong goniometers; however, they often have the advantage of higher stability, a larger homogeneous area in the sample and a larger range of temperature (see Chapter 2.6[link] ).

Devices for static high-pressure generation are more difficult to construct because of the obvious requirement for strong walls capable of withstanding the high pressure applied to the sample. There are several types of high-pressure device and they can be classified in several ways. The piston-and-cylinder (PaC) press is the oldest type of pressure generator. However, the pressure range is limited in most advanced constructions (of multilayer negatively strained cylinders, like one shown in Fig. 2.7.1[link]) to 3.0 GPa (Baranowski & Bujnowski, 1970[link]; Besson, 1997[link]; Dziubek & Katrusiak, 2014[link]). PaC presses are ideal for volumetric measurements on a sample enclosed in the cylinder and for generating pressure in a hydrostatic medium transmitted through a capillary to other external high-pressure chambers containing the sample and optimized for a chosen measurement method, usually optical spectroscopy and diffraction. The external devices include chambers for loading the PaC with gas, which is either the hydrostatic medium or the sample itself (Tkacz, 1995[link]; Rivers et al., 2008[link]; Couzinet et al., 2003[link]; Mills et al., 1980[link]; Yagi et al., 1996[link]; Kenichi et al., 2001[link]). In some pressure generators, a cascade of two or three PaC presses is applied for highly compressible pressure-transmitting media (gases) before the final setup stage.

[Figure 2.7.1]

Figure 2.7.1 | top | pdf |

A cross section through a piston-and-cylinder device with a shrink-fitted double cylinder. In this design, the bottom piston (stopper F) is in the fixed position and only the top piston (A) is pushed into the cylinder by a hydraulic press. The main components of the device are: piston (A), inner cylinder (B), outer supporting shell (C), brass and rubber sealing rings (D), sample (E) and stopper (F).

The PaC press can be considered as the prototype of other large-volume presses (LVPs). The PaC press consists of a cylinder closed at both ends with pistons, sealed with gaskets. The attainable pressure depends mainly on the tensile strength of the cylinder and of the gasket. The cylinder can be strengthened by the process of frettage, i.e. inducing tensile strain in the outer part and compressive strain inside (Onodera & Amita, 1991[link]). This can be achieved by autofrettage, when a one-block cylinder is purposely overstrained to the point of plastic deformation and the deformation residues result in the required strain. Likewise, the cylinder can be built of shrink-fitted inner and outer tubes (the outer diameter of the inner tube is slightly larger than the inner diameter of the outer tube, which must be heated to assemble the cylinder) or of cone-shaped tubes (with a cone half-angle of ca 1°) pushed into one another to generate the frettaging strains. Alternatively, a coil of several layers of strained wire or tape can be wound around the cylinder, or the cylinder can be compressed externally to counteract its tensile strain simultaneously with the load being applied to the pistons (Baranowski & Bujnowski, 1970[link]). The load against the cylinder walls can be reduced by containing the sample in a capsule of soft incompressible material, usually lead (Bridgman, 1964[link]). Cylinder chambers with externally generated pressures up to 0.4 GPa (Blaschko & Ernst, 1974[link]) and PaC cells capable of generating 2 GPa (Bloch et al., 1976[link]; McWhan et al., 1974[link]) have been used for neutron diffraction, and a beryllium cylinder has been used for X-ray diffraction on protein crystals to 100 MPa (Kundrot & Richards, 1986[link]). The range of pressure up to a few hundred megapascals is often described as medium pressure. There are sample-environment chambers with externally generated medium pressure that are designed for in-house powder diffractometers operating in the Bragg–Brentano geometry (Koster van Groos et al., 2003[link]; Whitfield et al., 2008[link]).

If the cylinder length is reduced and the gasket reinforced by compression of the conical pistons, the girdle press is obtained (Fig. 2.7.2a[link]). Its optimized modification is the belt apparatus (Fig. 2.7.2b[link]). The girdle and belt presses generate pressures of about 10 GPa and can be internally heated to about 1500 K, and hence they have been used widely to synthesise materials. However, the opacity of the girdle/belt and anvils allows no access for X-ray or neutron beams between the anvils. This disadvantage is alleviated in the opposed-anvils press, operating on the massive-support principle, where the beams can pass through the gasket material. After the first record of a simple version of the opposed-anvils experiment in the mid 19th century performed in order to measure the effect of medium pressure on the electric conductibility of wires by Wartmann (1859[link]), the opposed anvils were extensively developed and applied to much higher pressure by Bridgman (1935[link], 1941[link], 1952[link]). He also equipped them with a pyrophyllite gasket separating the anvil faces (Bridgman, 1935[link]), and in this form they are commonly known as Bridgman anvils (Fig. 2.7.2[link]c). In the 1960s, the flat faces of the Bridgman anvils were modified to so-called toroidal anvils (Fig. 2.7.2d[link]), where the sample space is considerably increased by hemispherical depressions at the anvil centre and surrounded by a groove supporting the gasket and preventing its extrusion (Khvostantsev, 1984[link]; Khvostantsev et al., 1977[link], 2004[link]; Ivanov et al., 1995[link]). Anvils with a spherical sample cavity only, so-called Chechevitsa anvils, preceded the construction of toroidal anvils. Toroidal anvils were optimized for neutron diffraction by adding a small pneumatic press called the Paris–Edinburgh cell (Besson et al., 1992[link]). Toroidal anvils enabled neutron diffraction studies up to 50 GPa and 3000 K (Kunz, 2001[link]; Zhao et al., 1999[link], 2000[link]; Redfern, 2002[link]). Experiments on magnetic systems in a similar pressure range and at low temperature were performed in a very different design of opposed anvils, the sapphire Kurchatov–LBB cell, shown in Fig. 2.7.3[link] (Goncharenko & Mirebeau, 1998[link]; Goncharenko, 2004[link]).

[Figure 2.7.2]

Figure 2.7.2 | top | pdf |

Cross sections of (a) the girdle anvil, (b) the belt anvil, (c) the Bridgman anvil and (d) the toroid anvil. The gaskets are dark grey, the tungsten carbide elements are pale grey and the sample chamber is yellow.

[Figure 2.7.3]

Figure 2.7.3 | top | pdf |

A schematic view of the opposed-sapphire anvil of the Kurchatov–LBB cell designed for neutron diffraction on magnetic materials (Goncharenko, 2004[link]).

More complex LVPs have been based on multi-anvil presses (Liebermann, 2011[link]). These are usually very large devices capable of containing tens of cubic centimetres of sample. The sample is encapsulated and pressurized between anvils sealed with some kind of gasket. The attainable pressure depends on a number of factors, including the applied load and the strength of the anvils, which are made of steel, tungsten carbide, sapphire or sintered diamond; the maximum pressure depends inversely on the sample volume. Multi-anvil presses (Huppertz, 2004[link]; Liebermann, 2011[link]) – tetrahedral, trigonal–bipyramidal, cubic (Akimoto et al., 1987[link]) and octahedral (Onodera, 1987[link]) – are optimized for larger sample volumes and for the high temperatures required for the synthesis of hard materials, especially diamond (Hazen, 1999[link]). The multi-anvil presses are used for diffraction studies. The sample can be either contained in a capsule or mixed with a pressure-transmitting pseudo-hydrostatic medium, which is inert and a weak absorber of X-rays. The sample is accessed by the X-ray beam between the anvils through a weakly absorbing sealing material, such as amorphous boron, magnesium oxide, corundum or pyrophyllite. Like the opposed-anvil presses, multi-anvil LVPs can be used effectively for X-ray diffraction at synchrotrons and neutron sources. However, these large installations also require (apart from intense primary beams) powerful translations for their precise centring relative to the primary beam and diffractometer axes. The main advantage of an LVP is stable and homogenous internal heating up to about 2000 K (Besson, 1997[link]). Such stable conditions are particularly valuable for high-pressure synthesis and crystallization, for example of diamonds (Hazen, 1999[link]).

2.7.4. The diamond-anvil cell (DAC)

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The invention of the DAC revolutionized high-pressure studies, diversified their scope, greatly simplified the experimental procedures, increased the range of pressure and temperature, and initiated constant growth in the number of high-pressure structural studies, starting in the 1960s and continuing up to today. The DAC is built from a pair of opposing diamond anvils and a vice to generate their thrust. The sample is compressed between the culets of the anvils. Since its inception, the DAC has been modified and redesigned frequently, in order to adapt it to new experimental techniques or to take advantage of the parallel progress in scientific equipment. The original DAC built at the National Bureau of Standards (Maryland, USA) was used for infrared spectroscopy. Another DAC designed for powder diffraction experiments was made of beryllium, a relatively strong metal which weakly absorbs short-wavelength X-rays (Weir et al., 1959[link]; Bassett, 2009[link]). The DAC, with steel frames and beryllium discs supporting the anvils, is still in use today.

The original and most efficient concept applied in the operation of the DAC was that the incident beam enters the pressure chamber through one diamond anvil and the reflections leave through the other anvil; this mode of operation is often referred to as transmission geometry. Together with the diamond anvils, Be discs constitute windows for the X-rays. However, beryllium has several disadvantages. It is the softest and weakest of the materials used in DAC construction, it softens at about 470 K, beryllium oxide is poisonous, and machining beryllium is difficult and expensive. Therefore, except for the pioneering DAC design by Weir et al. (1959[link]), Be parts were initially limited to disc supports for the anvils. Moreover, polycrystalline Be discs produce broad reflection rings and a strong background, and the small central hole in the disc obscured optical observation of the sample. In many modern DACs the beryllium discs have been completely eliminated, and the diamond anvils are directly supported by steel or tungsten carbide platelets (Konno et al., 1989[link]; Ahsbahs, 2004[link]; Boehler & De Hantsetters, 2004[link]; Katrusiak, 2008[link]). For this purpose new diamond anvils, exemplified in Fig. 2.7.4[link], were designed. Anvils of different sizes, culet dimensions, height-to-diameter ratios and other dimensions can be adjusted for the experimental requirements, such as the planned pressure range and the opening angles of the access windows.

[Figure 2.7.4]

Figure 2.7.4 | top | pdf |

Cross sections of three types of diamond anvil used in high-pressure cells: the brilliant design (supported either on the table or on the crown rim), the Drukker design (supported on the table and crown) and the Boehler–Almax design (supported on the crown).

Another DAC was independently designed for X-ray powder diffraction by Jamieson et al. (1959[link]). In their DAC, the incident beam was perpendicular to the axis through the opposed anvils, and the primary beam passed along the sample contained and squeezed directly (no gasket was used) between the culets. The reflections were recorded on photographic film located on the other side of the DAC, perpendicular to the incident beam. This geometry was described as either panoramic, perpendicular or transverse. The transverse geometry is also used with beryllium or other weakly absorbing gaskets (Mao et al., 1998[link]). Other DACs, for example where both the incident beam and the reflections pass through one diamond anvil, were also designed (Denner et al., 1978[link]; Malinowski, 1987[link]); however, the transmission geometry is most common owing to its advantages. In the transmission geometry the uniaxial support of the anvils leaves a window for optical observation of the sample, as well as for spectroscopic and diffractometric experiments along the cylindrical pressure chamber. Therefore, at present most DAC designs operate in transmission geometry.

The DAC construction can generally be described as a small vice generating thrust between opposed anvils. In the first DACs designed in the late 1950s, no gasket nor hydrostatic fluids were used and the sample was exposed to strong anisotropic stresses. Van Valkenburg (1962[link]) enclosed the sample in a hole in a metal gasket, filled the hole with hydrostatic fluid and sealed it between the culets of the anvils. This most significant development of the miniature high-pressure chamber opened new possibilities for all sorts of studies under hydrostatic conditions, in particular powder and single-crystal diffraction studies. Since then, the gaskets have become an intrinsic part of the DAC. The hydrostatic conditions in the DAC have been used to grow in situ single crystals from the melts of neat compounds (Fourme, 1968[link]; Piermarini et al., 1969[link]) and from solutions (Van Valkenburg et al., 1971a[link],b[link]). Now it is a common method for in situ crystallization under isothermal and isochoric conditions (Dziubek & Katrusiak, 2004[link]; Bujak et al., 2004[link]; Fabbiani et al., 2004[link]; Fabbiani & Pulham, 2006[link]; Budzianowski & Katrusiak, 2006a[link],b[link]; Dziubek et al., 2007[link]; Paliwoda et al., 2012[link]; Sikora & Katrusiak, 2013[link]).

The original designs of the DAC (Weir et al., 1959[link]; Jamieson et al., 1959[link]) were later adapted to various purposes. Significant modifications take advantage of new designs of diamond anvils and their supports. Initially, the brilliant-cut diamonds of traditional design, but with the culet ground off to form a flat thrust surface parallel to the table, were used (Fig. 2.7.4[link]). Culets of 0.8 mm in size can be used to about 10 GPa, 0.4 mm culets to about 50 GPa, 0.1 mm culets to about 100 GPa and 0.02 mm (20 µm in diameter) or even smaller (Akahama et al., 2014[link]; Akahama & Kawamura, 2010[link]; Dalladay-Simpson et al., 2016[link]) culets can be used for the megabar 200–400 GPa range. The megabar range requires bevels on the culets to protect their edges from very high strain and damage. The bevels are about 6–7° off the culet plane and the ratio of bevel-to-culet diameters is between 10 and 20. Also, the gasket material, the hole diameter and its height, being a fraction of the hole diameter, are of primary importance. Double bevels can be used to release the strain further, but it appears that a value of about 400 GPa is the maximum pressure attainable in the conventional DAC (c-DAC).

The pressure limits of the c-DAC are surpassed in a double-stage DAC (ds-DAC), in a toroidal DAC (t-DAC) or by shock compression. In the ds-DAC a pair of small anvils, constituting a microscopic DAC (m-DAC, also described as second-stage anvils), is contained inside the c-DAC. The micro-anvils are prepared from diamond or amorphous diamond using the focused ion-beam technique (Sakai et al., 2015[link], 2018[link]). For another type of ds-DAC, employing microscopic diamond hemispheres (Dubrovinsky et al., 2012[link]; Dubrovinskaia et al., 2016[link]), pressures exceeding 1 TPa have been reported. In the t-DAC, each diamond culet is modified in such a way that an ion-beam-eroded groove surrounds the central micro culet (Dewaele et al., 2018[link]; Jenei et al., 2018[link]; Mao et al., 2018[link]).

At present, the DAC most commonly applied in laboratories is a miniature Merrill–Bassett DAC, where the anvils are installed on two triangular frames driven by three screws along three sliding pins (Merrill & Bassett, 1974[link]). Analogous designs with two or four thrust-generating screws are also in use. The original Merrill–Bassett DAC was equipped with a pair of brilliant-cut 0.2 carat diamonds with polished culets (Fig. 2.7.4[link]) and the anvils were supported on Be discs. The Merrill–Bassett DAC is optimized for use with automatic diffractometers. It contains no rocking blocks but allows translation of one of the anvils. The light weight and small size allow the Merrill–Bassett cell to be routinely used on single-crystal diffractometers. This simple DAC design is suitable for experiments up to about 10 GPa. Dedicated DACs for higher pressure have rocking supports for the diamonds, in the form of either hemispheres or half-cylinders (Fig. 2.7.5[link]).

[Figure 2.7.5]

Figure 2.7.5 | top | pdf |

A cross section through the central part of a diamond-anvil cell, schematically showing the main elements applied in various designs. Usually, either beryllium backing plates or steel/tungsten carbide backing plates with conical windows are used. One of the plates can be translated and the other rocked in all directions (the hemispherical rocking mechanism). In other designs, one of the anvils can be rocked around and translated along one axis, and the other anvil rocked and translated in the perpendicular direction (two perpendicular hemi-cylindrical mechanisms). The usual thickness of the beryllium plate is 3 mm or more, and most constructions allow a window opening of about 40° to the DAC axis. The thickness of the diamond window (the table-to-culet distance) is usually about 1.5 mm.

A very fine adjustment of the anvils and fine and remote pressure control can be obtained in a membrane DAC, where the thrust is generated by a metal membrane operated with gaseous helium or nitrogen (Letoullec et al., 1988[link]; Chervin et al., 1995[link]). Owing to the ideally coaxial thrust generation by the membrane and the stable supports of the anvils, usually in the form of a piston and cylinder, the membrane DAC is suitable for generating pressures of hundreds of gigapascals. The membrane DAC can be operated remotely through a flexible metal capillary, which is advantageous for spectroscopy and both powder and single-crystal diffraction experiments at synchrotrons.

2.7.5. Variable-temperature high-pressure devices

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One of the most common interests in extreme conditions combines high pressure and high temperature. Several techniques for simultaneously controlling both pressure and temperature have been developed (Fei & Wang, 2000[link]). The DAC can be heated externally (with respect to the sample chamber between the anvils' culets) when the entire DAC is placed in an oven or in a hot stream of air from an electrical heater (Fourme, 1968[link]; Allan & Clark, 1999[link]; Podsiadło & Katrusiak, 2008[link]; Bujak et al., 2008[link]). External resistance-wire heaters placed immediately around the diamond anvils and the gasket are often used (Bassett & Takahashi, 1965[link]; Takahashi et al., 1982[link]; Adams & Christy, 1992[link]; Eremets, 1996[link]; Moore et al., 1970[link]; Hazen & Finger, 1982[link]; Besson, 1997[link]; Dubrovinskaia & Dubrovinsky, 2003[link]; Fei & Wang, 2000[link]). External heating can routinely operate up to about 673 K. Its main advantages are stability, reliable measurement of temperature and high homogeneity of temperature in the chamber. The disadvantages include the relatively low temperature range and the large mass of the DAC mechanical parts that are heated. Their thermal expansion can cause loss of pressure. This does not apply to the membrane DAC, where a constant thrust from the membrane is transmitted to the anvils. A sophisticated externally heated DAC in an atmosphere of inert gases is capable of operating between 83 and 1473 K (Bassett et al., 1993[link]).

A very small turnbuckle DAC, about 6 mm in diameter, was originally constructed of plastic and hardened beryllium–copper alloy (BERYLCO 25) in order to perform magnetic measurements at low temperature in the small bore of a superconductive quantum interference device (SQUID) (Graf et al., 2011[link]; Giriat et al., 2010[link]). These are at present the smallest designs that can be used for X-ray diffraction studies, with the whole DAC cooled by commercial low-temperature gas-stream attachments. Alireza & Lonzarich (2009[link]) built another miniature DAC for high-pressure magnetic measurements in a SQUID.

Temperatures of several thousand kelvin can be achieved by internal heating, where the sample absorbs the focused light beam of a laser (Bassett, 2001[link]; Ming & Bassett, 1974[link]; Shen et al., 1996[link]) or is heated by a thin wire passing through the chamber or its immediate surroundings, either in the gasket walls (Boehler et al., 1986[link]; Mao et al., 1987[link]; Zha & Bassett, 2003[link]; Dubrovinsky et al., 1998[link]) or in the culets of intelligent diamond anvils (Bureau et al., 2006[link]). Composite resistance gaskets, with a platinum chamber wall acting as a 35 W resistance heater, can increase the temperature to over 2273 K (Miletich et al., 2000[link], 2009[link]). Laser beam(s) focused through the DAC anvil(s) onto the sample (Boehler et al., 2001[link]) can heat it to over 3273 K. This requires that the laser beam, or several beams, or a fraction of their energy, be absorbed in the sample. In order to increase the absorption, the sample can be mixed with another compound, for example gold powder. The main disadvantage of laser heating is inhomogeneous distribution of the temperature within the sample.

Much smaller temperature gradients, of a few kelvin at 2773 K, can be obtained in large-volume presses (LVPs). The multi-anvil LVP has traditionally been applied for the synthesis of diamond, which requires stable conditions of both high pressure and high temperature (Hazen, 1999[link]; Liebermann, 2011[link]). In the LVP, a resistance heater installed inside the chamber can provide stable control of the temperature for days, while the pressure is controlled by a hydraulic press. Owing to the large sample volume, the diffraction pattern can be quickly recorded. Most often, energy-dispersive diffraction is applied for the beams entering and leaving the pressure chamber through the gasket material between the anvils. LVPs are generally very large and heavy, which contrasts with the compact construction of the Paris–Edinburgh and Kurchatov–LLB pressure cells (Besson et al., 1992[link]; Goncharenko, 2004[link], 2006[link]). Both these opposed-anvil cells can be placed in cryostats, and they can be used for either energy- or angle-dispersive diffraction of neutrons or X-rays. The Kurchatov–LLB cell has been optimized for neutron diffraction studies of magnetic structures at high pressure and low temperature (Goncharenko & Mirebeau, 1998[link]; Goncharenko et al., 1995[link]).

2.7.6. Soft and biomaterials under pressure

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Interest in the effects of pressure on biological materials is connected to the processing of food and the search for methods of modifying the structure of living tissue and its functions. Soft biological compounds, including proteins, membranes, surfactants, lipids, polymer mesophases and other macromolecular assemblies present in living tissue, are susceptible to pressure, which can affect the molecular conformation and arrangement with relatively low energies of transformation (Royer, 2002[link]). Medium pressure suffices for protein coagulation, as observed for egg white at 0.5 GPa by Bridgman (1914[link]). However, single crystals of egg-white lysozyme survived a pressure of several gigapascals (Katrusiak & Dauter, 1996[link]; Fourme et al., 2004[link]), which was connected to the concentration of the mother liquor used as the hydrostatic fluid. Cells with externally generated pressures up to about 200 MPa for diffraction measurements on single crystals in a beryllium capsule (Kundrot & Richards, 1986[link]) and on powders contained between beryllium windows (So et al., 1992[link]) have been built. Powder diffraction studies have also been performed on samples frozen under high pressure and recovered to ambient pressure (Gruner, 2004[link]). High-pressure studies can be conveniently performed in the DAC, but because of the usually weak scattering of macromolecular samples, synchrotron radiation is preferred for such experiments (Fourme et al., 2004[link]; Katrusiak & Dauter, 1996[link]).

2.7.7. Completeness of data

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The steel parts of the DAC can restrict access of the incident beam to the sample and can obscure the exit of reflections. For a typical DAC working in transmission mode, the incident beam can be inclined to the DAC axis by up to about 25–40°, for the full opening of the window of 50–80°, respectively. In most DACs the collimator and detector sides are symmetric, so the opposing conical windows have the same opening angle. This limited access to the sample can affect the completeness of diffraction data for low-symmetry crystals, which can then pose considerable difficulties in solving and refining crystal structures from single-crystal measurements.

The restricted access of the primary and diffracted beams to the sample can conveniently be described by the concept of the reciprocal lattice (Fig. 2.7.6[link]). The initial orientation of the crystal in the DAC defines the accessible region of the reciprocal lattice in such a way that the Ewald sphere can be inclined to the initial direction of the incident beam by up to the maximum window opening angle, denoted αM. The sample can be accessed from both sides of the DAC (by rotating the DAC by 180°) and thus the accessible region of reciprocal space has the form of a round flat cushion, with surfaces touching at the cushion centre [described as a donut cake by Merrill & Bassett (1974[link])], as shown in Fig. 2.7.6[link]. In the directions perpendicular to the DAC axis, the maximum coordinate [d_{yz}^*] = 2λ−1 sin αM of reciprocal vectors is for many crystals larger than the resolution of the data (for a typical DAC, αM = 40°, which for organic crystals or other weakly scattering substances is less than required, as the data measured with Mo Kα radiation for molecular crystals often extend up to a maximum θ of only about 25°). However, access to the reciprocal lattice is significantly limited along the DAC axis (perpendicular to the flat cushion). In this direction, only those reflections can be accessed for which[d_x^* = 2\lambda^{-1} \sin^2 (\alpha_M/2) ,]where [d_x^*] is the maximum coordinate of accessible reciprocal vectors along the xL axis running from the sample to the radiation source in the laboratory reference system, λ is the wavelength, and αM is the opening angle of the window measured from the DAC axis (or the maximum inclination of the DAC axis to the incident beam). For example, a DAC with a full window opening angle of 2αM = 60° limits the laboratory reciprocal x coordinate to 0.1885 Å−1 when λ(Mo Kα) = 0.71073 Å is used; if the crystal x* axis is aligned along the laboratory xL axis, and if the crystal a* = 0.10 Å−1, then the maximum Bragg reflection index |h| is 1. If the wavelength is decreased to λ(Ag Kα) = 0.56 Å, the maximum dx increases to 0.2392 Å−1 and reflections with index h = 2 can be recorded.

[Figure 2.7.6]

Figure 2.7.6 | top | pdf |

A diamond-anvil cell, showing the 40° half-angle opening of the conical windows and the reciprocal space accessed for a single-crystal sample and Mo Kα or Ag Kα radiation. In this schematic drawing, the window cones intersect at the disc-shaped sample (yellow–blue shaded rectangle) and around it the Ewald spheres of reciprocal radii corresponding to Mo Kα and Ag Kα wavelengths are drawn. The shape of the two yellow profiles meeting at the reciprocal 000 node is the cross section through the torus-like accessible volume of reciprocal space for Mo Kα radiation; this torus is circularly symmetric about the DAC axis. The grey shape is likewise the accessible space for Ag Kα radiation. Both are at the same resolution of 1/dhkl = 1/0.8 Å−1 (corresponding to θ angles of 26.4° for Mo Kα radiation and 19.7° for Ag Kα). For a powdered sample, all reciprocal-space nodes contained within the resolution sphere (dotted circle) can be recorded. The DAC windows and the sample are shown at the initial `zero' position, when the DAC axis coincides with the primary beam; the red arrows indicate the rotation of the DAC, sample and Ewald sphere to the limiting 40° angle.

Although the accessible region of the reciprocal lattice depends strongly on the DAC design, the final completeness of the data also depends on several other factors: (i) the symmetry of the sample crystal; (ii) the sample orientation; and (iii) the wavelength of the X-ray radiation. Therefore, the DAC is ideally suited to high-pressure studies of simple and high-symmetry crystals. The Laue-class symmetry of cubic crystals is either [m\bar 3] or [m\bar 3m], and in most cases the whole of the required resolution falls within the accessible flat-cushion reciprocal region. Thus, the completeness in high-pressure experiments on cubic samples mounted in the chamber at a random orientation is not limited. For hexagonal and tetragonal samples, the crystal orientation is very significant. The maximum completeness can be obtained when the hexagonal or tetragonal axis is perpendicular to the DAC axis. Then the sample reciprocal axis c* is located along the flat-cushion plane. When two axes of a monoclinic or ortho­rhombic crystal are at 90° to the DAC axis, a considerable portion of the symmetry-independent part of the reciprocal lattice is not accessible. This reduces the completeness of the data, even though the redundancy of the data is increased. Optimum orientation of the sample can double the completeness compared with experiments measured for the same sample with its axes aligned along the DAC axis and plane.

The completeness of the data can be increased by collecting several data sets for samples oriented differently in the DAC and merging these data (Patyk et al., 2012[link]). This purpose can also be achieved by placing several crystal grains at different orientations in the high-pressure chamber, and then separating their reflections, indexing them and merging.

When the powder diffraction method is used, this problem of completeness is irrelevant. As shown in Fig. 2.7.7[link], for an ideal powder with randomly oriented grains all reciprocal-lattice nodes can be represented as spheres and they all satisfy the Bragg diffraction condition. The main problem occurring for samples with low symmetry and long lattice constants is overlapping reflections. The intensity of the powder reflection rings is low, because only a small fraction of the sample volume, less than one part per million, contributes to the intensity at a specific point on the reflection ring. Furthermore, the sample volume in the DAC is very small. For these reasons, powder X-ray diffraction in the laboratory usually provides only qualitative information. After the introduction of synchrotron radiation and area detectors, powder diffraction became one of most efficient methods of high-pressure structural studies.

[Figure 2.7.7]

Figure 2.7.7 | top | pdf |

A schematic illustration of the reciprocal space associated with a sample enclosed in a diamond-anvil cell (DAC). For clarity, the sizes of the sample and diamond anvils have been increased. The Ewald sphere is drawn for the sample only and cubic symmetry with an a parameter of 10 Å has been assumed. Of the reciprocal lattice of the sample, only the layer of hk0 nodes is shown as small circles within the resolution limit of 1/dhkl = 1/0.8 Å−1. The Ewald spheres of the diamond anvils have been omitted, and only the layer of nodes hk0 of the detector anvil is shown as yellow rectangles. Owing to its short unit-cell parameter of 3.57 Å and [Fd\bar3m] symmetry, there are few diamond reflections in the pattern. Note the displaced origins of the reciprocal lattices of the sample and of the detector anvil (the anvil on the detector side) as a result of the off-centre positions of the anvil. For a powdered sample, each node is distributed on a sphere. In this drawing, the spheres are represented by circles only for nodes 100, 110, 200, 210, 220 and 300. The other node spheres contained within the chosen resolution limit have been omitted for clarity; for a triclinic sample, the hk0 layer would include 266 powder reflections.

2.7.8. Single-crystal data collection

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It is essential that a crystal sample is centred precisely on the diffractometer. Optical centring of a crystal is hampered by the limited view of the sample through the DAC windows in one direction only and by the strong refractive index of diamonds. Consequently, diffractometric methods of crystal centring are more precise for DAC centring. Hamilton's method comparing the diffractometer setting angles of reflections at equivalent positions (Hamilton, 1974[link]) was modified for the purpose of the DAC by King & Finger (1979[link]) and then generalized for any reflections, not necessarily at equivalent positions (Dera & Katrusiak, 1999[link]). These methods are very precise, but they require the approximate orientation matrix (UB matrix) of the sample crystal (Busing & Levy, 1967[link]) to be known and the reflections to be indexed. This information was determined at the beginning of an experiment when traditional diffractometers with a point detector were used. However, nowadays diffractometers with area detectors are used, and generally the crystal orientation is not determined before collecting the diffraction data. To meet these requirements, a new efficient and semi-automatic method was devised, whereby the diffractometer measures a sequence of shadows of the gasket on the CCD detector and calculates the required corrections to the DAC position along the goniometer-head translations (Budzianowski & Katrusiak, 2004[link]). Precise centring can only be achieved for very stable goniometer heads that do not yield under the weight of the DAC (Katrusiak, 1999[link]).

The mode of data collection for a sample enclosed in a DAC can affect the data quality considerably. Data for a bare crystal on a four-circle diffractometer with a scintillation point detector were measured in the so-called bisecting mode, where the ω angle [diffractometer-axes positioning angles ω, χ, ϕ and θ of the Eulerian cradle will be used here (Busing & Levy, 1967[link]), unless otherwise noted] was fixed to 0° and not used in the process of crystal positioning. In other words, the shaft ϕ and circle χ lie in the plane bisecting the angle formed by the incident beam and the reflection actually measured. The bisecting mode was optimal for avoiding collisions between the diffractometer shafts and detector, and also minimized absorption effects for most vertically mounted samples. However, these features are irrelevant for samples enclosed in a DAC. It was shown by Finger & King (1978[link]) that the DAC absorption of the incident and reflected beams is a minimum when the Eulerian goniometer ϕ axis is not used and is always set to 0°. Hence, this is called the ϕ = 0° mode. The ϕ = 0° mode also minimizes the effect of the sample being shadowed by the gasket edges (Katrusiak, 2008[link]). Moreover, in the ϕ = 0° mode the DAC axis always lies in the diffraction plane of the diffractometer, which gives maximum access to the reciprocal-lattice nodes (Fig. 2.7.6[link]).

The advent of area detectors facilitated high-pressure experiments considerably and extended the range of attainable conditions to simultaneous very high pressure and temperatures of several thousand kelvin. Single-crystal experiments are easier because the diffraction data can be recorded before the orientation matrix UB of the crystal is determined (Busing & Levy, 1967[link]; Finger & King, 1978[link]). The recorded data can thus be analysed after the experiment and all relevant structural models can be tested. The use of area detectors shortens the data-collection times for both single-crystal and powder diffraction measurements, and this is particularly efficient with the extremely intense X-ray beams provided by synchrotrons. In single-crystal experiments, several or even tens of reflections are partly scanned through or fully recorded in one image. Although these reflections are not each recorded at their optimum diffractometer settings, corresponding to the ϕ = 0° mode setting described above, the redundancy of the data is increased and the intensities can be corrected for the absorption coefficients derived from differences between equivalent reflections. It is also advantageous that simultaneous diffraction events in the sample crystal and in one or both of the diamonds, which occur sporadically and weaken the recorded reflections, can be eliminated by comparing the intensities of the same reflection measured at several ψ angle positions as well as the equivalent reflections. Equivalent reflections measured at different positions are particularly useful for eliminating systematic errors in the data collection.

It is important that the so called `run list', defining the diffractometer setting angles and scan directions for the detector exposures, takes into account the ϕ = 0° mode of the DAC orientations, for which access to the DAC is still on average at its widest and the DAC absorption and gasket-shadowing effects are on average the smallest. Most importantly, such an optimum setting can be executed with a four-circle diffractometer, and cannot be done on simplified diffractometers with the ϕ shaft fixed at a χ angle of about 50°. Even fewer reflections can be accessed when the DAC is rotated about one axis only, which is still the case for some laboratory and synchrotron diffractometers.

2.7.9. Powder diffraction with the DAC

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The DAC is often described as the workhorse of high-pressure research, owing to its versatile applications, low cost, easy operation and unrivalled attainable static pressure. However, the small size of the DAC chamber, containing sample volumes between 0.025 mm3 for pressure to about 5 GPa, 0.005 mm3 to about 10 GPa and less than 3 × 10−6 mm3 for the megabar range, can be disadvantageous for powder diffraction studies. The disadvantages include the inhomogeneous distribution of temperature within the sample (particularly as it remains in contact with a diamond, which is the best known thermal conductor) and nonhydrostatic strain (often due to the technique of generating pressure by uniaxial compression of the chamber). In some samples close to the melting curve some grains increase in size at the expense of others, partly or fully dissolving, so the number of grains may be insufficient for obtaining good-quality powder diffraction patterns. This difficulty can be partly circumvented by rocking the DAC during the experiment about the ω axis. On the other hand, for a sample consisting of tens of grains it is possible to perform multi-grain analysis by merging the diffraction patterns to give the equivalent of single-crystal data. High-pressure powder diffraction patterns can also be affected by a low signal-to-noise ratio, too few crystal grains, and their preferential orientation in the DAC uniaxially compressed chamber. The preferential orientation is particularly significant when the grains are elongated and their compressibility is anisotropic; these effects can be further aggravated by the non-hydrostatic environment. Powder reflections are much weaker in intensity than the equivalent single-crystal reflections from the same sample volume. Small sample volumes are compensated for by the powerful beams available at synchrotrons. At present, high-pressure powder diffraction experiments are mainly carried out at synchrotrons by energy-dispersive (Buras et al., 1997a[link],b[link]; Baublitz et al., 1981[link]; Brister et al., 1986[link]; Xia et al., 1990[link]; Oehzelt et al., 2002[link]) and angle-dispersive methods (Jephcoat et al., 1992[link]; Nelmes & McMahon, 1994[link]; Fiquet & Andrault, 1999[link]; Crichton & Mezouar, 2005[link]; Mezouar et al., 2005[link]; Hammersley et al., 1996[link]). Angle-dispersive methods are currently preferred to the energy-dispersive method owing to their higher resolution and simpler data processing. However, the energy-dispersive method requires less access for the X-ray beams probing the sample, and hence it is often preferred for studies in the megabar range (hundreds of gigapascals). For high-pressure powder diffraction studies in the laboratory, energy-dispersive methods are still preferred (Tkacz, 1998[link]; Palasyuk & Tkacz, 2007[link]; Palasyuk et al., 2004[link]). The main advantages of experiments at synchrotrons are:

  • (i) They have a very intense beam compared with traditional sealed X-ray tubes and modern micro-focus sources;

  • (ii) They offer the possibility of very narrow collimation of the beam, to a diameter of one or a few micrometres;

  • (iii) Very quick collection of high-quality diffraction data is possible, which is most useful for high-pressure and very high temperature data collections;

  • (iv) It is possible to measure diffraction data from very small samples, to reduce the dimensions of the DAC chamber and hence to increase the attainable pressure, which is inversely proportional to the chamber diameter;

  • (v) The microbeam can illuminate a small selected portion of the sample chosen for the investigation, which can be used to perform single-crystal diffraction on a selected grain or for X-ray tomography of the sample and its inclusions;

  • (vi) The beam diameter is smaller than the diameter of the chamber, which minimizes or even eliminates the effects of beam shadowing;

  • (vii) The X-ray wavelength is tuneable down to about 0.3 Å. This considerably increases the data completeness and reduces absorption effects in the sample and DAC.

Owing to these features, synchrotron beams are ideally suited for high-pressure diffraction experiments and some researchers have completely stopped using in-house laboratory equipment with sealed X-ray tubes. Historically, the first use of synchrotron radiation for high-pressure studies was reported by Buras, Olsen & Gerward (1977[link]) and Buras, Olsen, Gerward et al. (1977[link]). Conventional diffractometers with sealed X-ray tubes can be effectively used for preliminary powder diffraction experiments. For example, a new high-pressure phase of (+)-sucrose was found in this way (Patyk et al., 2012[link]), although the data were insufficient for any structural refinements.

Diffraction data are collected in single and multiple exposures, and the pressure is controlled remotely by inflating a membrane through a gas system. Currently assembled high-pressure powder diffraction synchrotron beamlines incorporate on-line pressure calibration using ruby fluorescence and, often, Raman spectroscopy.

2.7.10. Sample preparation

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Several basic techniques can be used to prepare a sample for a high-pressure experiment, for example:

  • (i) A solid sample can be mounted under ambient conditions in the high-pressure chamber together with the hydrostatic fluid, then sealed and pressurized;

  • (ii) A solid sample can be mounted under ambient conditions in the high-pressure chamber, condensed gas loaded at elevated pressure (Tkacz, 1995[link]; Rivers et al., 2008[link]; Couzinet et al., 2003[link]; Mills et al., 1980[link]; Yagi et al., 1996[link]; Kenichi et al., 2001[link]) or under cryogenic conditions, and the sample sealed and further pressurized by gasket compression;

  • (iii) A liquid sample can fill the whole chamber volume under ambient conditions, or condensed gases or their mixtures can be loaded at elevated pressure, and after sealing the DAC the sample is frozen under isothermal conditions;

  • (iv) A crystal of the pure compound or of a solvate can precipitate from the mixture (solution) when compressed isothermally – the crystal can be in the form of a single crystal or a powder, fully or partly filling the DAC chamber;

  • (v) Samples completely filling the DAC chamber can be compressed isothermally or undergo isochoric treatment, but strains can be generated in a single crystal or in the grains of a compressed powder conglomerate by anisotropic thermal contraction/expansion; this strain can be avoided by having an excess of the hydrostatic component of the mixture;

  • (vi) A solid powdered sample can be mixed with a powder of another compound, which is much softer than the sample and is used as a pseudo-hydrostatic medium (halite and MgO are often used for this purpose) – this technique is mainly used for cubic or isotropic samples in large-volume presses, where (pseudo)isotropic strain and pseudo-spherical compression minimize the effect of preferential orientation in the sample.

Preferential orientation can significantly hamper the quality of powder diffraction data, and corrections for this effect should be applied in the Rietveld refinement. All Rietveld refinement programs include preferential orientation models, which fit the data with satisfactory results (McMahon, 2004[link], 2005[link]; Filinchuk, 2010[link]).

2.7.11. Hydrostatic conditions

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Hydrostatic conditions in the sample chamber are essential for good-quality high-pressure diffraction data. They are equally important for single-crystal and powder diffraction experiments. To secure hydrostaticity, the sample is submerged in a hydrostatic medium. The pressure and temperature ranges of the planned experiment depend on the hydrostatic properties of the applied medium. Eventually all substances solidify because of crystallization or vitrification (Piermarini et al., 1973[link]; Eggert et al., 1992[link]; Grocholski & Jeanloz, 2005[link]), which can lead to damage of single crystals, anisotropic strain in powder grains and inhomogeneity of pressure across the sample. It is also important to protect a solid sample from dissolution in the hydrostatic fluid. The dissolved sample can lose its required features (such as shape, polymorphic form or chemical composition) and recrystallize at higher pressure in an undesired form. For example, a fine powder may recrystallize into a few large and preferentially oriented grains. Another potential problem can arise from reactions between the sample and the hydrostatic medium. For example, a pure compound can form solvates incorporating molecules of the hydrostatic fluid (Olejniczak & Katrusiak, 2010[link], 2011[link]; Andrzejewski et al., 2011[link]; Tomkowiak et al., 2013[link]; Boldyreva et al., 2002[link]; Fabbiani & Pulham, 2006[link]). This has also been observed for helium and argon penetrating into the structures of the fullerenes C60 and C70 (Samara et al., 1993[link]) and into arsenolite As4O6 (Guńka et al., 2015[link]). High-pressure crystallization of water in the presence of helium leads to an inclusion compound interpreted as ice XII. Therefore, the hydrostatic medium should be carefully chosen for a specific experiment, depending on the sample solubility, the pressure range and the type of investigation, whether a mounted-sample study, or in situ crystallization or reaction (Sobczak et al., 2018[link]; Półrolniczak et al., 2018[link]).

Many minerals and inorganic samples hardly dissolve at all and a commonly applied pressure-transmitting medium is a mixture of methanol, ethanol and water (16:3:1 by volume), hydrostatic to over 10 GPa at 296 K (see Table 2.7.1[link]); separately, pure methanol crystallizes at 3.5 GPa, ethanol at 1.8 GPa and water at 1.0 GPa. If a sample dissolves well in methanol, ethanol and water, other fluids can be selected (Piermarini et al., 1973[link]; Angel et al., 2007[link]). Liquids like glycerine (hydrostatic to 3 GPa) and special inert fluids, such as silicone oil (Shen et al., 2004[link]; Ragan et al., 1996[link]), Daphne oil (Yokogawa et al., 2007[link]; Murata et al., 2008[link]; Klotz et al., 2009[link]), or condensed gases, like helium, argon and hydrogen (Tkacz, 1995[link]; Dewaele & Loubeyre, 2007[link]), can be used. Alternatively, a saturated solution of the sample compound, for example in a methanol–enthanol–water mixture, can prevent sample dissolution, but on increasing the pressure the compound can precipitate in the form of a powder or single crystals. One can choose to load an excess of the sample into the chamber before filling it up with the hydrostatic fluid, which would dissolve only some of the sample.

Table 2.7.1| top | pdf |
The (pseudo)hydrostatic limits of selected media at 296 K (Holzapfel, 1997[link]; Miletich et al., 2000[link])

MediumFreezing point (GPa)(Pseudo)hydrostatic limit (GPa)Reference
4:1 Methanol:ethanol 9.8 Angel et al. (2007[link])
16:3:1 Methanol:ethanol:water 10.5 Angel et al. (2007[link])
Anhydrous propan-2-ol 4.2 Angel et al. (2007[link])
Neon 4.7 19 Klotz et al. (2009[link])
Argon 1.2 9/35 Bell & Mao (1981[link])/You et al. (2009[link])
Helium 11.8 70/150 Bell & Mao (1981[link])/Dewaele & Loubeyre (2007[link])
Hydrogen 5.7 177 Mao & Bell (1979[link])
Nitrogen 2.4 13 LeSar et al. (1979[link])
Glycerol 1.4 Angel et al. (2007[link])
Glycerin 3.0 Hazen & Finger (1982[link])
Glycerin   4.0 Tateiwa & Haga (2010[link])
Fluorinert FC84/87 7.0 Klotz et al. (2009[link])
Petroleum ether 6.0 Mao & Bell (1979[link])
Isopropyl alcohol   4.3 Piermarini et al. (1973[link])
1:1 Pentane:isopentane 7.4 Piermarini et al. (1973[link])
Silicone oil, viscosity 0.65 cSt 0.9 Angel et al. (2007[link])
Silicone oil 14 Klotz et al. (2009[link])
Daphne oil 7373   2.3 Murata et al. (2008[link])
Daphne oil 7474   3.7 at 296 K/6.7 at 273 K Klotz et al. (2009[link])/Tateiwa & Haga (2010[link])
Vaseline 2.0 Tateiwa & Haga (2010[link])
NaCl 0.05/25 Tateiwa & Haga (2010[link])/You et al. (2009[link])

In situ crystallization at high pressure requires good, though not necessarily very good, solvents. Also, co-crystallizations can be performed in the DAC, and in this case the product that is obtained can depend on the solvents used and their concentration. Pressure effectively modifies intermolecular interactions, and new solvates can be obtained depending on the concentration of the substrates. It can be tricky to avoid co-crystallization of some compounds; in these cases a range of hydrostatic fluids has to be tried. A mixture of petroleum ethers, silicone or Daphne oils can be a good choice. Daphne oil, consisting mainly of alkylsilane (Murata et al., 2008[link]), has the rare feature of negligible thermal expansion, which is particularly useful for low-temperature high-pressure experiments: the DAC can be loaded under normal conditions and then pressurized and cooled to the required temperature, e.g. in a cryostat, without significant loss of pressure due to contraction of the medium.

The hydrostatic conditions can be checked by inspecting the width of reflections from the sample (full width at half-maximum, FWHM, is usually plotted), the width of the ruby fluorescence R1 line and the R1R2 line separation (You et al., 2009[link]). The pressure homogeneity can be checked by measurements for several ruby chips mounted across the DAC chamber. Nonhydrostatic conditions can cause inconsistent results and difficulties in their interpretation, which can prompt the researcher to consider changing the hydrostatic medium.

For hard samples, some departure from hydrostatic conditions is often acceptable. It is assumed that for a hard sample the nonhydrostatic compression component is small in a much softer medium, for example, hard corundum studied in soft NaCl. On the other hand, it may be easier to prepare a sample under normal conditions by uniformly mixing the powder of the specimen with a pseudo-hydrostatic medium, rather than using hydrostatic liquids or gases. The diffraction from the pseudo-hydrostatic medium powder can be used to monitor the pressure and measure non-hydrostaticity effects. Pseudo-hydrostatic solid media are often used for multi-anvil presses, where a solid sample facilitates loading and the uniaxial stress is not as drastic as in the opposed-anvil presses. Also, in high-temperature experiments the process of annealing reduces non-hydrostatic strain.

A relatively low nonhydrostatic effect was reported for argon frozen at 1.9 GPa: its pressure gradient up to 1% only is supported at 9 GPa (Bell & Mao, 1981[link]) and up to 1.5% at 80 GPa (Liu et al., 1990[link]). This illustrates how the pseudo-hydrostaticity limit can be extended depending on the hardness of the specimen, the type of high-pressure device and the acceptance of deviatoric stress in the sample.

At very high pressure, exceeding 60 GPa, no compounds persisting as liquids are known (cf. Table 2.7.1[link]). Diffraction data must then be corrected for a deviatoric stress component, causing the broadening of reflection rings and affecting their 2θBragg positions, when the uniaxial stress is not collinear with the incident beam (Singh, 1993[link]; Singh & Balasingh, 1994[link]; Singh et al., 1998[link]; Mao et al., 1998[link]). The effect of uniaxial stress can be reduced or eliminated by sample annealing, which is often applied to improve the hydrostaticity of the sample.

2.7.12. High-pressure chamber and gasket in the DAC

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A high-pressure device should be adjusted to the experiments planned, and in particular to the chemical activity of the sample. Gaseous hydrogen penetrates and dissolves in most metals, and therefore special alloys, such as beryllium bronze, have to be used for hydrogen setups. For some experiments non-metallic gaskets can be used, for example amorphous boron, corundum or diamond powders mixed with a resin. Owing to the insulating properties of such a gasket, the pressure dependence of the electric, dielectric and magnetic properties of the sample can be measured. Chemically aggressive samples can interact with the gasket material of the DAC chamber, and even with the diamond anvils, and this effect usually intensifies at high temperature and pressure. Consequently, both the sample and the high-pressure device can be affected. The erosion caused by an aggressive liquid can be considerably slowed down by its crystallization, which freezes the diffusion of molecules into the gasket. For example, in situ crystallization of halogen derivatives of acetic acid could only be performed in a DAC chamber with tungsten gaskets (Gajda & Katrusiak, 2009[link]). In these experiments, the gasket was gradually eroded by the acid, but after its crystallization the measurements could be performed over several days. In order fully to prevent erosion of the gasket, it can be coated with a layer of inert material, for example gold or platinum. Alternatively, a composite chamber can be prepared: after pre-indenting the gasket and drilling a hole at the centre of the indentation, a piece of gold wire can be fitted to the hole, and after pressing into a hole in the DAC again, a smaller hole can be drilled through this inset. A DAC chamber formed in this way has a gold lining and can be resistant to aggressive compounds.

2.7.13. High-pressure neutron diffraction

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Neutron scattering is an indispensable and complementary technique in materials research (see Chapter 2.3[link] ), particularly for compounds containing heavy elements that strongly absorb X-rays, or light-atom weak X-ray scatterers (e.g. see Goncharenko & Loubeyre, 2005[link]). However, the flux of neutron sources, both reactors and spallation targets, is several orders of magnitude lower than that of X-rays, even from traditional sealed X-ray tubes. Moreover, the scattering cross sections of neutrons are on average two orders of magnitude smaller than for X-rays (Bacon, 1975[link]). These two considerations conflict with the requirement of small sample volume preferred for high-pressure devices. Consequently, a prohibitively long measurement time would be required to obtain meaningful neutron diffraction data from the DAC in its original form and size-optimized for X-ray studies. Therefore, initially, the designs of high-pressure devices for neutron scattering studies were based on typical large-volume presses: gas bombs with external multi-stage pressure generators, and piston-and-cylinder, multi-anvil and belt presses (Worlton & Decker, 1968[link]; Bloch et al., 1976[link]; McWhan et al., 1974[link]; Srinivasa et al., 1977[link]; Besson, 1997[link]; Klotz, 2012[link]). The sample volume in the Bridgman-type opposed-anvil press, with flat anvils separated by a gasket of pipestone, was increased severalfold by making a recess at the centre of the pressure chamber of the so-called Chechevitsa anvils (Stishov & Popova, 1961a[link],b[link]). The sample volume was further increased in toroid anvils by grooves supporting the gasket around the central recess (Khvostantsev et al., 1977[link]). This made them ideal for powder diffraction neutron measurements on samples of about 100 mm3 to above 10 GPa in a Paris–Edinburgh hydraulic press (Besson et al., 1992[link]; Besson, 1997[link]). The application of sintered diamond anvils increased this pressure range. High-pressure cells in a form optimized for neutron diffraction can contain between several cubic millimetres and a few cubic centimetres of sample volume. Such a large sample volume naturally limits the pressure range of cells used for neutron diffraction, compared with the DAC used for X-rays. However, the pressure range has increased considerably for neutron diffraction experiments during recent decades, to over 20 GPa in a moissanite anvil cell (Xu et al., 2004[link]; Dinga et al., 2005[link]), and to 40 GPa in a high-pressure cell capable of operating in helium cryostats at 0.1 K and in magnetic fields up to 7.5 T (Goncharenko, 2006[link]; Goncharenko et al., 1995[link]). High-pressure high-temperature cells for neutron diffraction are usually equipped with internal heaters capable of exceeding 1500 K (Zhao et al., 1999[link], 2000[link]; Le Godec et al., 2001[link], 2002[link]).

It is particularly advantageous for the construction of large presses for neutron studies that most of the materials used have very low absorption of neutrons. There are also metals (vanadium, aluminium) with very low scattering lengths, and it is possible to obtain alloys (Ti66Zr34) with the scattering length scaled to zero. This allows access of the neutron beam to the sample and exit of reflections. In a Paris–Edinburgh cell operating in the time-of-flight mode, the incident beam enters the pressure chamber through the tungsten carbide anvil, along its axis, and the reflections leave the chamber through the gasket along the slit between the anvils with approximately ±6° opening (Besson et al., 1992[link]; Takahashi et al., 1996[link]). In this operation mode, highly neutron-absorbing anvils made of sintered cubic boron nitride (cBN) can also be used (Klotz, 2012[link]). Alternatively, the monochromatic angle-dispersive mode of operation, with the incident and diffracted beams passing through the slit between the anvils, is possible but it is less efficient with regard to the use of the full spectrum of neutrons. The application of a focused neutron beam and the time-of-flight technique allow the use of small sample volumes of a fraction of a cubic millimetre in compact opposed-anvil high-pressure cells (Okuchi et al., 2012[link]). Two DACs were recently optimized for neutron diffraction on single crystals. Owing to the application of a white neutron beam, the structure of a crystal 0.005 mm3 in volume was determined. All reflections could be recorded because of the smaller Merrill & Bassett (1974[link]) design made of neutron-transparent beryllium–copper alloy (Binns et al., 2016[link]). Another design with a wide access to the sample for the primary and diffracted beams has been successfully used at a hot-neutron source (Grzechnik et al., 2018[link]).

2.7.14. Pressure determination

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Pressure determination inside a high-pressure sample chamber is most straightforward in piston-and-cylinder devices, where the force applied to the piston and its surface area are known. Pressure is the force per unit area, with corrections for the friction between the cylinder wall and the piston (particularly significant above 1 GPa) and for the buoyancy of the piston, marginally important for all high pressures. Several types of mechanical pressure gauge are available. In the Bourdon gauge, a spiral metal tube that is pressurized inside unwinds and moves a pointer around a precise scale. Electrical resistance gauges are most often based on a manganin alloy sensor. The resistance of manganin changes at the rate of 2.4 × 10−5 GPa−1, although precise calibration depends on the alloy composition and it changes with the age of the sensor. The resistance of manganin depends only very weakly on temperature.

The most common pressure calibration method used for the DAC is the fluorescence pressure scale of the ruby R1R1 at 0.1 MPa is the reference; λ0 = 694.2 nm) and R2 (at 0.1 MPa, λR2 = 692.8 nm) lines (Forman et al., 1972[link]; Barnett et al., 1973[link]; Syassen, 2008[link]; Gao & Li, 2012[link]). Synthetic ruby with a Cr3+ concentration of 3000–5500 p.p.m., illuminated with green laser light, is commonly used. Inclusions of spinels make natural ruby unsuitable as a pressure gauge. A piece of ruby is usually crushed into small pieces and one or several small chips are placed in the DAC chamber close to the sample (Hazen & Finger, 1982[link]). Alternatively, small ruby spheres can be used for this purpose (Chervin et al., 2001[link]).

The linear pressure dependence of the ruby R1 fluorescence line was established according to the equation of state (EOS) of NaCl to 19.5 GPa:[P \, ({\rm GPa}) = 2.74 \Delta \lambda \, ({\rm nm}) ,]where Δλ = λR1 − λ0 (Piermarini et al., 1975[link]). The extension of the pressure range to 180 GPa, according to the equations of state of copper, gold and other metals, showed that P(Δλ) is quasi-linear:[P = 1904 [(\lambda/\lambda_0)^B - 1]/B ,]where B = 7.665 for quasi-hydrostatic and 5.0 for non-hydrostatic conditions (Mao et al., 1986[link], 1978[link]; Bell et al., 1986[link]).

The ruby fluorescence depends strongly on temperature (Barnett et al., 1973[link]; Vos & Schouten, 1991[link]; Yamaoka et al., 2012[link]) and a temperature change of about 6 K causes R1 line shifts equivalent to 0.1 GPa. The fluorescence-line dependence on temperature is much weaker for Sm2+:SrB4O7 (Lacam & Chateau, 1989[link]; Lacam, 1990[link]; Datchi et al., 1997[link]) and the other rare-earth-doped sensors listed in Table 2.7.2[link]. These sensors can be more sensitive to pressure than ruby, and together with ruby can be used simultaneously for both temperature and pressure calibration.

Table 2.7.2| top | pdf |
Luminescence pressure sensors, their electronic transition types (s = singlet, d = doublet) and rates of spectral shifts (after Holzapfel, 1997[link])

SensorTransitionλ0 (Å)dλ/dP (Å GPa−1)dλ/dT (× 10−2 Å K−1)(dλ/dP)/Γ (Å GPa−1)(dλ/dT)/(dλ/dP) (× 10−2 GPa K−1)
Cr3+:Al2O3 2E4A2/d 6942 3.65 (9) 6.2 (3) 4.9 17.0
Sm2+:SrB4O7 5D07F0/s 6854 2.55 −0.1 17.0 −0.4
Sm2+:BaFCl 5D07F0/s 6876 11.0 −1.6 4.8 −1.5
Sm2+:SrFCl 5D07F0/s 6903 11.2 (3) −2.36 (3) 5.8 −2.1
Eu3+:LaOCl 5D07F0/s 5787 2.5 −0.5 1.0 −2.0
Eu3+:YAG 5D07F1/d 5906 1.97 −0.5 0.7 −2.5

The calibration of most pressure gauges is based on comparisons of theoretical and shock-wave data (Holzapfel, 1997[link]), so the derived equations of state are used with an accuracy of about 5% up to 1 TPa. The EOS recommended by Holzapfel (1997[link]) is[P = [3K_0 (1 - x)/x^5] \exp [c_0 (1 - x)] , \eqno(2.7.1)]where x = a/a0 = (V/V0)1/3, c0 = 3(K0′ − 3)/2, a is the unit-cell dimension, V is the unit-cell volume, a0R and V0R are the reference parameters under ambient conditions (Table 2.7.3[link]), α0R is the thermal expansion coefficient, K0R is the bulk modulus, and K0′ = dK0/dP. dK0/dT = −3α0RK0δαR, where δαR = ∂(lnα)/∂(lnV)TR. Pressure can be computed by assuming constant K0′ and linear temperature relations for T close to or higher than TR = 300 K:[\eqalign{ a_0 (T) & = a_{0R} [1 + \alpha_{0R} (T - T_R)] , \cr V_0 (T) & = V_{0R} [1+ 3 \alpha_{0R} (T - T_R )] , \cr K_0 (T) & = K_{0R} [1 - \alpha_{0R} \delta_{\alpha R} (T - T_R)] .}]

Table 2.7.3| top | pdf |
Parameters recommended for pressure determination by EOS measurements

Various face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) metals are used as calibrants, with the EOS given by equation (2.7.1)[link] and the reference temperature TR = 300 K (after Holzapfel, 1997[link]).

Metala0R (pm)K0R (GPa)K0Rα0R (× 106 K)δαR
Al 404.98 (1) 72.5 (4) 4.8 (2) 23.0 (4) 5.5 (11)
Cu 361.55 (1) 133.2 (2) 5.4 (2) 16.6 (3) 6.1 (6)
Ag 408.62 (1) 101.0 (2) 6.2 (2) 19.2 (4) 7.1 (6)
Au 407.84 (1) 166.7 (2) 6.3 (2) 14.2 (2) 7.2 (6)
Pd 388.99 (1) 189 (3) 5.3 (2) 11.6 (4) 6.0 (11)
Pt 392.32 (1) 277 (5) 5.2 (2) 8.9 (4) 5.9 (l1)
Mo 314.73 (1) 261 (5) 4.5 (5) 5.0 (4) 5.2 (14)
W 316.47 (1) 308 (2) 4.0 (2) 4.5 (4) 4.7 (11)

The details of the parameterization are explained by Holzapfel (1991[link], 1994[link]) and listed for the simple face-centred (f.c.c.) and body-centred (b.c.c.) cubic metals in Table 2.7.3[link] (Holzapfel, 1997[link]). Powders of these metals can be mixed with the sample and its pressure can be calibrated according to the unit-cell dimension of the standard. The well known compressibilities of NaCl, CaF2 and MgO, in the form of either powders or single crystals, are also often used as internal pressure standards (Dorfman et al., 2010[link], 2012[link]; Dorogokupets & Dewaele, 2007[link]).

An independent pressure assessment can be obtained from standard materials undergoing pressure-induced phase transitions (Table 2.7.4[link]). This method is limited to just a few pressure points (Holzapfel, 1997[link]), but they can provide a useful verification of other pressure gauges.

Table 2.7.4| top | pdf |
Pressure fixed points at ambient temperature (after Holzapfel, 1997[link]; Hall, 1980[link])

P (GPa)Element transition
0.7569 (2) Hg freezing at 273 K
1.2 (1) Hg freezing at 298 K
2.55 (6) Bi I–II at 298 K
3.67 (3) Tl h.c.p.–f.c.c.
2.40 (10) Cs I–II
4.25 (1) Cs II–III
4.30 (1) Cs III–IV
5.5 (1) Ba I–II
7.7 (2) Bi III–IV
9.4 (3) Sn I–II
12.3 (5) Ba II–III
13.4 (6) Pb I–II
Onset of forward transition.
Centre of hysteresis.

Other methods of pressure calibration are still being developed. For example, it has been shown that very high pressure can be determined from the Raman shift of strained diamond-anvil culets (Akahama & Kawamura, 2004[link]). The strong piezochromic effect of visible colour changes in soft coordination polymers allows pressure calibration without spectrometers. These changes can proceed gradually (Andrzejewski & Katrusiak, 2017a[link]) and abruptly at phase transitions (Andrzejewski & Katrusiak, 2017b[link]). Another method of pressure calibration is based on the luminescence lifetime of lanthanide nanocrystals (Runowski et al., 2017[link]).

2.7.15. High-pressure diffraction data corrections

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Apart from the Lorentz and polarization (Lp) corrections routinely applied to reflection intensities measured for bare crystals (i.e. crystals not enclosed in environment devices), as well as other corrections like extinction and absorption in the sample, the effects of the high-pressure cell should additionally be accounted for. These effects mainly include absorption in the pressure-vessel walls, shadowing of the sample by the pressure-cell opaque elements and elimination of the reflections of the diamond anvils for measurements in a DAC. The set of corrections is usually described for the specific pressure vessel. For a typical DAC with the anvils (about 1.7 mm high) supported directly on the edges of conical steel or tungsten carbide windows, and for Mo K radiation, the absorption is quite uniform and varies between about 0.50 and 0.60, for the beams passing close to the DAC axis and those close to the conical window edge, respectively. This absorption is even smaller at the shorter wavelengths used for high-pressure X-ray diffraction studies at synchrotrons. For this reason the absorption correction for the DAC is often neglected.

The sample-shadowing correction accounts for the loss of intensity due to the sample being partly shadowed by the gasket edges. This effect can be avoided by choosing a sufficiently small crystal or by applying a sufficiently narrow beam, which would illuminate only the central part of the sample. Such microbeams are now routinely used at synchrotrons. For these reasons, synchrotron data are often used straightforwardly after applying just the Lp corrections and incident-beam variation and eliminating the diamond reflections. In fact there are very few diamond reflections because of the small unit cell and many systematic absences, and the DAC can be treated as a low-background cuvette for powder diffraction.

The corrections for absorption and gasket shadowing are very important for high-pressure data collection in the laboratory, where a sealed X-ray tube is used. Its beam is relatively weak and for this reason the quality of the data (signal-to-background ratio) is low, but can be improved by increasing the sample volume. Ideally, a sample that completely fills the DAC chamber secures the highest intensity of reflections. However, for large samples the shadowing of the incident and diffracted beams by the gasket is very significant and should be corrected for (Katrusiak, 2004a[link],b[link]).

The calculation of the so-called analytical corrections, obtained by dividing the high-pressure chamber into small pixels and calculating the beam's trajectory to and off each pixel, through all the DAC components (beryllium discs, if present, diamond anvils, hydrostatic fluid and sample) can precisely eliminate errors. Having the correct reflection intensities simplifies the structure solution of new phases and increases the accuracy of the refined structure. It has been shown that some incompleteness of accurate data does not cause systematic errors in the structural parameters (Dziubek & Katrusiak, 2002[link]). In most calculations of reflection intensity corrections, the cylindrical symmetry of the DAC about its axis is assumed (Katrusiak, 2001[link], 2004a[link],b[link]; Hazen & Finger, 1982[link]; Angel, 2004[link]; Kuhs et al., 1996[link]; Miletich et al., 2000[link]).

Diffraction measurements with area detectors have the advantage of collecting data with a considerable redundancy factor, which is often routinely used to calculate the so-called empirical absorption corrections, which are sometimes applied to a sample in a DAC. The intensities of powder diffraction reflections measured at synchrotrons with microbeams are often not corrected, particularly when the DAC axis is not significantly moved from the primary beam during data collection. The redundancy of the data also considerably reduces the effect of simultaneous diffraction events by the sample and one or two of the diamond anvils.

The most significant systematic errors in the diffraction of a sample in a DAC may be due to preferential orientation of the grains, which can occur for an anisotropic sample and non-hydrostatic conditions in the chamber. This effect can be accounted for in the process of Rietveld refinement (McMahon, 2004[link]; Filinchuk, 2010[link]), or may require repetition of the measurement after reloading a new sample into the DAC.

2.7.16. Final remarks

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During the last 100 years, and particularly during the last few decades, high-pressure diffractometric techniques have been developed covering a broad range of research in different fields of science. It is simply impossible to present all aspects of high-pressure methodology in one chapter. Many books, book chapters and scientific papers have been written on high-pressure research and therefore I have chosen to present a `flavour' of high-pressure crystallography, rather than concentrating on all its aspects. Readers interested in specific subjects can find the required information in a number of instructive books (Hazen & Finger, 1982[link]; Eremets, 1996[link]; Holzapfel, 1997[link]; Katrusiak & McMillan, 2004[link]; Boldyreva & Dera, 2010[link]; McMahon, 2012[link]) and in numerous articles in research journals. This chapter is only an introduction and gives some useful reference information for high-pressure crystallographers.

It should be stressed that the sample-preparation techniques for high-pressure studies are relatively demanding. Therefore, diffraction studies are often `adjusted' to the form of the sample obtained in the high-pressure device. In particular, powder diffraction, single-crystal and spectroscopic measurements can be conducted on some synchrotron beamlines (see e.g. Dera et al., 2013[link]). Many experimental techniques complementary to high-pressure crystallographic studies have not been mentioned here.

It can be concluded that, over the years, high-pressure research has become quite popular in materials science and at present all over the world there are hundreds or even thousands of scientists capable of performing high-pressure experiments. Their scientific output is significant, and can be used as a guide for those interested in specific types of high-pressure research.

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