2.1. Historical background

In hindsight, the construction of the DAC appears very simple and its operation obvious. It is amazing that such a small, plain and elegant device is capable of generating the highest static pressures achieved in a laboratory. Moreover, it seems that all the knowledge necessary for the DAC invention was known and published by P. W. Bridgman.³ He formulated the principle of massive support (Bridgman, 1937), constructed the opposed-anvils apparatus (so called Bridgman anvils) capable of generating a pressure of 10 GPa (Bridgman, 1950, 1952), and used a pipestone gasket for sealing and preventing extrusion of the sample from between the anvils. However, his anvils were large and made of carboloy (tungsten carbide cemented in cobalt), a material very hard and heat-resistant but in many respects inferior to diamond. Other milestones that led to the DAC invention were:

(i) application of diamond in high-pressure devices (Lawson & Tang, 1950; Jamieson, 1957);

(ii) designs of the opposed-diamond-anvils cell (DAC) (Jamieson et al., 1959; Weir et al., 1959);

(iii) application of a metal gasket in the DAC for obtaining hydrostatic pressure conditions (van Valkenburg, 1962);

(iv) invention of the ruby-fluorescence method for pressure calibration (Forman et al., 1972).

There were a considerable number of other very important developments, without which the DAC would not be such a versatile apparatus as it is today (for reviews, see Hazen & Finger, 1982; Jayaraman, 1983; Ahsbahs, 1987; Eremets, 1996; Holzapfel & Isaacs, 1997; Katrusiak & McMillan, 2004).

2.2. The key issue of right materials

The heart of any DAC is built of diamond. For ages, diamond has been known as the hardest material and assigned the highest grade of 10 on the Mohs scale. However, the jump to the next-hardest on the Mohs scale, corundum (grade 9), is a large one (Brazhkin et al., 2002). On the Knoop hardness scale, diamond is several times harder than corundum – on this absolute scale, the hardness of corundum is much closer to that of talc and graphite (grade 1 on the Mohs scale) than to diamond; and the resistance of diamond to abrasion (about 140000 on the Rosiwal scale) is over two orders of magnitude higher than that of corundum (1000). Thus, with respect to its hardness, diamond is the most suitable material for high-pressure cell construction. It also has other advantages: low absorption of short X-rays, linear absorption coefficient μ_diamond(Mo Kα) = 0.202 mm⁻¹, excellent transparency for visual radiation, and good transparency for UV and IR wavelengths (type IIA diamonds with low nitrogen content). Although diamonds are considered expensive, the cost of a typical DAC for X-ray diffraction, equipped with flawless ¼ carat brilliant anvils, amounts to a mere few percent of that of either a low- or a high-temperature attachment.

The DAC is a unique construction of the most advanced apparatus of its kind, ingenious and elegant in its simplicity, the most essential parts of which were well known to nearly everyone – the flawless brilliants like those in rings or jeweller's shops (Fig. 1). For X-ray diffraction applications, the diamond anvils are often mounted on beryllium discs, which in turn are centred in a steel vice with conical windows, like in a miniature Merrill–Bassett cell shown in Fig. 2 (Merrill & Bassett, 1974). The linear absorption coefficient for beryllium is very low for molybdenum radiation, μ_Be(Mo Kα) = 0.048 mm⁻¹, however the beams passing through the discs increase the background, produce powder diffraction rings and beryllium softens at about 500 K, which hampers applications at high temperature. Beryllium is also expensive and its oxide is poisonous. Therefore, the anvils are often mounted directly on the steel edges of the conical windows (Konno et al., 1989). The central hole in the beryllium disc or the conical window in the steel backing plates give convenient access for optical observations and spectroscopic measurements. The small volume of the DAC chamber eliminates any risk of explosions, associated with much larger cylinder-and-piston devices.

Up to today, flawless low-birefringence type IA ¼ carat (1 carat = 0.2 g) brilliant diamonds with a phased culet are most often used in DAC's (Fig. 1). In fact, the anvils of the first DAC's were gems confiscated from smugglers by customs agents and donated for research purposes (Piermarini, 2001). Other than brilliant shapes of diamond anvils have been designed in order to reduce the strains (which could result in failure of the anvils when generating pressure) or to facilitate mounting of the anvils. Some of these designs are illustrated in Fig. 3. In the standard Drukker anvil, its shape has been simplified and the table surface increased (Seal, 1984); the Boehler–Almax anvil was optimized for supporting its crown section on the precisely matching tungsten carbide backing plate (Boehler & De Hantsetters, 2004; Boehler, 2006); another design with the specially made anvils mounted on the crown section was described by Ahsbahs (2004). For pressures up to about 5.0 GPa, ordinary brilliant anvils supported on the crown facets by a steel backing plate (Fig. 4) are used in our laboratory. Diamond plates were also used for supporting the anvils (Yamanaka, Fukuda et al., 2001), and perforated diamond anvils are made for reducing absorption in Mössbauer spectroscopy (Dadashev et al., 2001). For Mbar pressures (above 100 GPa), bevelled culets reduce the stress concentration on the culet edges (Mao & Bell, 1978; Seal, 1984).

The DAC's are small – they can be mounted on stable goniometer heads (Fig. 2) and used for experiments with standard laboratory X-ray diffractometers (Fig. 5).

2.3. Principles of the DAC operation

The axial thrust produced by the DAC vice mechanism is transmitted to the large tables and crown edges of two opposed diamond anvils, and through the stressed anvils to the culets. The pressure exerted on the tables is multiplied by the factor of the ratio of the surface area of the supported table side to the culet surface, and squeezes the gasket and sample contained in the high-pressure chamber. For table and culet diameters of 3.0 and 0.7 mm, respectively, the ratio is 3.0²/0.7² ≈ 20, and to obtain the multiplication factor of 100 a 0.3 mm culet diameter would be required.

The chamber diameter is usually equal to half or less of that of the culet. Like in the seals designed by Bridgman, the pressure exerted by the culets on the gasket exceeds that in the pressurized sample, so the closure is self-sealing. The hardness of the gasket and anvil materials increases under compression. These principles of the DAC operation are the same in all designs, although they can be considerably modified for specific applications and adapted to the requirements of different probing methods. For the purpose of this paper, we will focus on X-ray diffraction crystallographic experiments, although DAC's are also used for high-pressure optical spectroscopy (IR, UV-VIS, Raman, NMR) and for other physical experiments, chemical reactions, syntheses of new materials, biological observations, and even as precision cuvettes in forensic investigations. The DAC is an ideal micro reaction chamber allowing optical observation of chemical transformations at many GPa pressures and varied temperatures (Nicol & Yin, 1984) – the progress in analytical methods allows successful characterization of minute amounts of products synthesized in this way. Pressure-induced transformations can be investigated in non-hydrostatic conditions when a substance is squeezed between the DAC culets (Fig. 6) and in hydrostatic conditions when the investigated substance is contained in a liquid (Fig. 7).

It follows from the massive support principle that a conical anvil can support a compressive stress nK, where K is the yield stress of the anvil material and n equals 1.0 for cylindrical anvils (semi-cone angle ξ equal to 0°) and 3.0 for ξ equal to 90°. The anvil culet is further supported by the plastically deformable gasket, which extrudes around the sloped pavilion to diameter D_ext, larger than the diameter of the culet, D, and additionally increases attainable pressure to P = 2Kln(D_ext/D) (Yousuf & Rajan, 1982; Dunstan, 1989; Dunstan & Spain, 1989).

2.4. DAC types and designs

There have been various DAC designs, optimized for the measurement technique, sample requirements and other thermodynamical conditions (low or high temperature). X-ray diffraction can be performed on single crystals and powders (Meade & Jeanloz, 1990; McMahon, 2004; Parise, 2004), as well as on intermediate cases of `bad powders' with large crystalline grains. Only the DAC's for diffraction studies will be briefly classified and exemplified below. Laboratory X-ray diffractometers and those used at synchrotron beamlines considerably differ too (Prewitt et al., 1987; Mao et al., 1988; Nelmes et al., 1992; Fiquet & Andrault, 1999; Crichton & Mezouar, 2004; Katrusiak, 2004a). At synchrotrons, very intense X-ray beams can be collimated to a few micrometres, thus the problem of the beam shadowing by the gasket is considerably reduced; the huge intensity of the beam allows efficient and quick experiments to be performed by the powder method on very small samples, which allows experiments at very high pressures and varied temperatures; by applying very short wavelengths (of about 0.3 Å), one can considerably increase the completeness of accessible data; and owing to the low divergence of the beam and large sample–detector distance the overlapping ratio of powder diffraction rings in the powder experiments is minimized.

The advantage of laboratory set-ups is that they allow one to perform high-pressure studies with no restrictions in the countries and institutions that have restricted access to synchrotrons. At present, single-crystal X-ray diffraction is the easiest technique to implement and the most precise method for studying crystal structure at elevated pressure in a laboratory. Most X-ray laboratories are equipped with single-crystal angle-dispersive diffractometers, which can be easily adapted to high-pressure studies.

Generally, elastic scattering studies can be classified into monochromatic and polychromatic methods, and also as angle-dispersive and energy-dispersive, and single-crystal and powder techniques. All these methods are applied in structural studies. In the energy-dispersive set-up, the polychromatic beam is diffracted on the powdered sample and at a given direction an energy-discriminating detector measures the intensity of reflections. This is convenient for high-pressure measurements because only narrow windows are required for the primary and diffracted beams. Energy-dispersive techniques are often used for powder X-ray diffraction measurements in laboratories, and also for neutron powder diffraction (time-of-flight method). However, the angle-dispersive methods are more precise for X-rays, and most X-ray laboratories are equipped with angle-dispersive diffractometers, for both single-crystal and powder diffraction. Angle-dispersive powder diffraction is superior to single-crystal studies in this respect because a complete set of data can be measured for a given DAC-window opening. Moreover, the single crystal may be difficult to grow, can be fragile and is often destroyed at phase transitions, and powder diffraction facilitates studies of transformations of such materials. The diffracted beams from small powder samples are very weak and therefore this method is preferably used at synchrotron facilities. However, powder diffraction with DAC may pose some difficulties due to the small size of the sample (few powder grains) and preferred orientation in the compressed or recrystallized powder.

The construction of the DAC vice (i.e. the thrust-generating mechanism) is adjusted to the applied diffraction method. The DAC's for angle-dispersive diffraction measurements are usually classified: (i) according to the positions of the windows for the incident and diffracted beams, as: transmission (Merrill & Bassett, 1974; Keller & Holzapfel, 1977) and transverse (Schiferl, 1977; Malinowski, 1987; Ahsbahs, 1987); (ii) according to the thrust-generating mechanism as: lever-arm (Weir et al., 1959), (2-, 3-, 4- etc.) screws and gliding bolts (Merrill & Bassett, 1974), double lever (Keller & Holzapfel, 1977), or inflatable membrane (Chervin et al., 1995); (iii) according to the range and method of controlling temperature as: cryogenic, externally/internally/laser heated DAC's; and (iv) according to other specific features and applications, like magnetic field transparent, for IR, NMR, Mössbauer spec­tros­copies, or a miniature DAC for four-circle diffractometers and cryostats.

Most of the DAC's used for diffractometric studies operate in transmission mode, when the primary beam enters the pressure chamber through one of the anvils and the reflection leaves through the opposite anvil. Other modes of the DAC operation are also possible: a transverse mode, when the primary and diffracted beams pass through the same diamond anvil (Malinowski, 1987), and perpendicular mode, when the beams pass through the gasket (Ahsbahs, 1987). The advantage of the transmission DAC's is that they are very simple, allow a convenient optical insight into the chamber, minimize the gasket shadowing and are convenient in operation. All DAC's consist of two blocks made of steel (or another strong alloy) in various ways supporting the diamond anvils, and of a mechanism for generating the thrust between them (three screws in the Merrill–Bassett cell and a membrane in the membrane cell shown in Fig. 2).

3.1. Choosing gasket, hydrostatic fluid, diamonds and DAC

Depending on specific measurement – the planned range of pressure, sample solubility, strength and scattering power etc. – appropriate DAC design, gasket, hydrostatic fluid and other experimental details can be chosen. For most routine single-crystal high-pressure experiments in the pressure range to about 5 GPa, a miniature DAC designed by Merrill & Bassett (1974) is a very convenient choice (Fig. 4); the gasket can be made of 0.25 mm steel, tungsten or hard alloy foil, with a hole diameter of 0.30–0.40 mm when diamond culets of 0.7–0.8 mm in diameter are used. The choice of the hydrostatic fluid depends on its pressure of solidification and on the solubility of the sample crystal (Piermarini et al., 1973; Angel et al., 2007).

3.2. Pressure generation

Pressure is generated when the DAC chamber filled with the sample and hydrostatic fluid is sealed and squeezed between the anvils and deformed gasket, as shown in Fig. 8. Generally, it is difficult to predict exactly how the gasket would deform when squeezed between the culets. However, the attainable pressure strongly depends on the applied dimensions of the culets and gasket. The main strength of the high-pressure chamber relies on the gasket contained between the culets, as the strongly compressed gasket material is much harder than at atmospheric pressure and the gasket surfaces are strongly supported owing to their large friction against the pressing culets. On the other hand, the thickness of the gasket (height of the DAC chamber, h) is inversely proportional to the attainable pressure, as the force acting on the gasket wall is proportional to its surface (Fig. 8). Thus one can draw a simplified diagram, shown in Fig. 9, of the attainable pressure depending on the ratio of 2h/(D − d), where h is the height of the pressure chamber, D is the culet diameter and d is the diameter of the high-pressure chamber.

The plots in Fig. 9 also illustrate that one can modify the chamber dimensions during experiments by so-called pressure cycling. In this technique, one increases pressure to a certain point, after which pressure is released (partly or completely) and increased again. In this new cycle, the starting chamber dimensions are modified. Moreover, many metals and alloys exhibit the work-hardening property and increase their strength when deformed several times.

Also, another technique, called pre-indentation of the gasket, is commonly applied (the blue arrow on the abscissa axis in Fig. 9). In some laboratories, the blank (not drilled) gasket is pre-indented in the DAC, after which the hole is drilled at the centre of the indentation (Hazen & Finger, 1982; Miletich et al., 2000). Then the gasket is re-mounted in the DAC in exactly the same orientation. The pre-indentation increases the strength of the gasket material, allows the chamber dimensions to be adjusted (thickness of the foil), and improves the chamber sealing at the initial stages of pressure generation. A simpler reverse sequence of pre-indenting is also applied (Katrusiak, 1999): first the hole is drilled and then the gasket is centred on the diamond culet with the sample crystal and ruby chip already mounted, then gently pressed with the second anvil to check centring, and then after filling the chamber with hydrostatic fluid an air bubble is left inside and the gasket is squeezed. The air bubble allows control over the chamber sealing and allows one to reduce the diameter of the chamber by the plastic compression of the gasket. Then a cycling procedure can be applied, as described above.

Because of the large forces applied on the hard gasket material, the edges of the anvils are exposed to very high stress and can break when generating pressure above 10 GPa – in such experiments, bevelled culets should be used to avoid damage of the anvils (Mao & Bell, 1978; Seal, 1984).

3.3. Pressure calibration

The determination of pressure in the DAC chamber posed a considerable problem for several years after the DAC was invented: the chamber volume was very small, and the range of attainable pressures exceeded by over an order of magnitude the pressures obtained by any static methods before. Pressure in the DAC cannot be assessed from the applied load because it is difficult to predict the distribution of forces and plastic and elastic deformations in the DAC mechanical parts, in the anvils and their backing plates, and in the gasket. The pressure assessed in this way was usually highly inaccurate (e.g. Brash, 1965a,b; Bujak et al., 2004; Bujak & Katrusiak, 2004). Other methods developed and used for calibrating pressure in the DAC are briefly described below.

Fixed-point scale based on the known freezing and solid–solid phase-transition pressures of internal standards, such as n-decane (m.p. = 0.30 GPa at 300 K), chloroform (0.54 GPa), n-hexane (1.04 GPa), ethanol (2.22 GPa), Si (T_c = 12.5 GPa at 300 K), ZnSe, ZnS, GaP and NaCl (30.0 GPa). Several of the initially accepted points (those without pressures given here) proved highly inaccurate later (Piermarini & Block, 1975; Piermarini, 2001).

Internal diffraction standard allows the pressure determination from the known equation of state. The diffraction pattern of a small single crystal or powder of the standard is measured simultaneously with that of the sample. This is a convenient method for powder studies and single-crystal experiments using two-dimensional detectors. In the case of point-detector diffractometers, the single-crystal internal standard required tedious separation and indexing of the standard and sample reflections (not to mention those from the diamond anvils) and re-measuring them in order to obtain required accuracy of the unit-cell-volume determination, which could consume one or two days for a single pressure point. With the CCD detector, the automatic indexing procedure of reflections occasionally produces the unit cell of ruby (used as the fluorescent standard; see below) as the first choice, instead of that of the sample investigated. High-symmetry strongly scattering crystals without phase transitions in the required pressure range can be used, for example NaCl (below 29.5 GPa), CsCl (to 30.0 GPa), CaF₂ (to 9.5 GPa) or quartz (SiO₂) or MgO (Yagi, 1985; Birch, 1986; Angel, 1993; Angel et al., 1997). For megabar domain and for high-temperature studies, powders of Fmm and Imm symmetric metals (Au, Pt, Pd, Al) can be used (Bell et al., 1986).

Fluorescence techniques considerably facilitated the pressure calibration for crystallographic experiments. In this method, a small chip of the calibrant is placed inside the DAC chamber, and then the pressure-induced change of its characteristic fluorescence band measured spectroscopically. Most often used for this purpose is the measurement of batochromic R_1,2-doublet shift, Δλ, in the ruby fluorescence (at ca 6942 and 6927 Å, with small differences up to a few Å depending on the ruby sample); the pressure–Δλ relation is linear to nearly 20 GPa in the form: Δp = 0.2740 (16) × Δλ GPa, Δλ in Å (Forman et al., 1972; Barnett et al., 1975; Piermarini et al., 1975); a quasi-linear relation in the form Δp = 1904[(λ/λ₀)^B − 1]/B, where B is 7.655 for quasi-hydrostatic compression and 5 for nonhydrostatic compression, extends the ruby fluorescence scale to 180 GPa (Bell et al., 1986). The measurement of the R_1,2 shift is quick and can be performed with a typical Raman spectrometer or with commercially available small spectrometers especially designed for pressure calibration, and a small green laser (second harmonic of a YAG 4 mW laser is used in our laboratory). Other optical pressure sensors are also in use. The R₁ line shift is temperature dependent (Δλ/Δp = 0.068 Å K⁻¹), which can cause systematic errors for overheated samples. In another pressure sensor, SrB₄O₇:Sm²⁺, the emission line at 6854 Å is narrower than in ruby, hardly temperature dependent (Δλ/Δp =  0.001 Å K⁻¹), and Δp  =  0.3922Δλ GPa, Δλ in Å (Lacam & Chateau, 1989; Leger et al., 1990; Datchi et al., 1997).

Infrared pressure gauges were devised to facilitate high-pressure IR spectroscopy. In the 1960's, IR spectroscopy became popular for high-pressure research, but the introduction of laser excitation made Raman spectroscopy on small samples more efficient; then commercialized Fourier-transform spectrometers with fast-response detectors revived the IR pressure studies. The pressure gauges devised for IR studies in DAC are dilute ca 3% solutions of nitrite or nitrate ions in sodium bromide (Klug & Whalley, 1983). Recently, it was shown that quartz mode 795 cm⁻¹ can be used as a pressure sensor to about 20 GPa (Chervin et al., 2005).

3.4. Data correction

The intensity of reflections from the crystal enclosed in the DAC should be corrected for Lorentz–polarization effects, the absorption of the DAC windows, absorption of the crystal itself, and shadowing of the sample crystal by the gasket (Hazen & Finger, 1982; Kuhs et al., 1996; Angel et al., 2000; Katrusiak, 2004b,c). Computer programs for applying these corrections have been written and are applied (Kuhs et al., 1996; Katrusiak, 2001, 2004b; Angel, 2004). When data with high redundancy are available, it is also possible, by checking the consistency of the Bragg angles and intensities of symmetry-equivalent reflections measured at varied positions of the DAC (and different ψ angles), to identify the reflections `colliding' with the edges of the windows, superimposed with the diamond reflections, or weakened by the simultaneous diffraction effects in the sample and one or two diamond anvils (Loveday et al., 1990). The R_int factor calculated after applying the corrections is a good measure of the quality of the corrected data. These data can be used like ordinary data, albeit only partly complete, for further stages of crystallographic calculations.

The application of the DAC with beryllium supporting plates for the anvils increases the background and somewhat lowers the transmission of the DAC (Figs. 10 and 11). On the other hand, the opening angle of the DAC with anvils supported on the edges of steel conical windows usually has a considerably smaller access for the beams onto the sample and a reduced completeness of the data that can be recorded.

3.5. Structure solution from high-pressure data

High-pressure data sets of reflection intensities recorded for low-symmetry sample crystals enclosed in the DAC are usually partly incomplete (Merrill & Bassett, 1974), as illustrated in Fig. 12. Generally, the completeness of data depends on the Laue-group symmetry of the sample crystal, its orientation, and window openings of the DAC, as explained above. For cubic crystal samples, and hexagonal or tetragonal crystals oriented with [001] direction perpendicular to the DAC axis, the completeness can approach 100%. The completeness of data attainable from one experiment decreases with decreasing Laue-class symmetry of the sample, and for triclinic samples can be lower than 30%. Nonetheless, standard methods of solving the structure can be applied, like the Patterson search or direct methods. Despite incomplete data for orthorhombic, monoclinic and triclinic samples, direct methods yielded correct solutions for all organic crystals investigated in our laboratory. For example, the new high-pressure ethynylbenzene triclinic phase, space group P with Z = 6 and 24 symmetry-independent carbon atoms (Dziubek et al., 2007), and the ortho­rhombic polymorph of 1,4-diazabicyclo[2.2.2]octane bromide, space group Cmc2₁ (Budzianowski & Katrusiak, 2006b), were solved straightforwardly by direct methods.

It appears that the toroidal distribution of accessible reflections from the sample enclosed in the DAC encompasses the reflections involved in the triple invariant relations and suffices for determining the reflection phases in this subset. The triple relations combine the reflections with indices h₁ = (h₁k₁l₁), h₂ = (h₂k₂l₂) and h₁ ± h₂ = (h₁ ± h₂, k₁ ± k₂, l₁ ± l₂). In reciprocal space, the nodes that are linear combinations of h₁ and h₂ are confined to the plane determined by vectors h₁ and h₂. Thus such invariant relations can be formed for the planes of reciprocal-space nodes. The set of such planes of nodes, which are inclined to the DAC axis by less than half of the angle of the DAC window-opening cones, approximate the toroidal region accessible for the DAC. Moreover, for most h₁ and h₂ vectors in all of the accessible toroidal region, their sum h₁ + h₂ is contained in this region, too. Thus the shape of the reciprocal-space-accessible region is favourable for direct methods, and this is reflected in the successful application of direct methods in high-pressure structural analyses.

4.1. From analogue to digital two-dimensional detectors

The first single-crystal high-pressure X-ray diffraction measurements with a DAC were performed by using a Buerger precession camera and diffraction patterns recorded photographically – the high-pressure studies on crystalline H₂O ice VI (Block et al., 1965) and chloroform (Fourme, 1968) were measured in this way. The recording of photographs on the precession camera requires that the crystal be precisely oriented such that the reciprocal plane be parallel to the film (one of the reciprocal vectors preferably along the precession axis and another vertical). The alignment of a bare crystal on the precession camera was accomplished in several steps. First, the crystal was mounted on a goniometer head in the approximately aligned position, then the crystal was more precisely adjusted by observing it through a microscope, and finally by performing a preliminary precession photograph from which final precise adjustments could be measured. The alignment of the crystal in the DAC was more difficult because of the limited possibility of controlling the orientation of the crystals in the DAC (particularly those grown by pressure freezing) and difficult microscopic observation of the crystal on the camera. After aligning the crystal in the DAC, a Laue-cone photograph and a few accessible reciprocal-lattice sections (perpendicular to the DAC axis) could be recorded. These data were sufficient for determining the crystal symmetry and the position and orientation of small molecules and ions in the crystal structure.

In the mid 1970's automatic four-circle diffractometers were applied to high-pressure single-crystal X-ray diffraction studies (Merrill & Bassett, 1974). The diffractometers were equipped with scintillation detectors and the measurement consisted of several stages. The crystal centring was performed optically with the aid of a microscope. The main difficulty was caused by the viewing of the crystal sample being restricted to one direction along the DAC axis. Thus the optical centring of the sample was difficult and usually was not precise. Any further steps required that the orientation matrix of the crystal (UB matrix) be determined. For finding the initial set of reflections, either a rotation photograph was made or a peak-hunting procedure performed. Then the reflections had to be indexed and the UB matrix could be determined and refined (Busing & Levy, 1967). With the UB matrix determined, one could refine the crystal centring by applying the diffractometric centring technique, which is much more reliable than the optical centring for the DAC. In the diffractometric technique, the corrections in the crystal position are derived from the offsets of the reflection positions. In the original version of the method, the selected reflections were measured at four or eight equivalent positions (Hamilton, 1974; King & Finger, 1979) and more recently a general procedure based on an arbitrary set of reflections was developed (Dera & Katrusiak, 1999). After centring the crystal, the UB matrix could be re-determined and more reliable unit-cell dimensions obtained. This was very important because the crystal positioning errors and restricted access to the reciprocal lattice of the sample often considerably lowered the precision of the UB matrix and affected the measurements of reflection intensities.

The accessible reflections were measured one by one. Whereas a bisecting mode of data collection was applied for bare crystal samples (i.e. the ω axis fixed at the 0° position, where the χ circle bisected the angle formed by the incident and reflected beams in the diffraction plane), Finger & King (1978) showed that for the DAC the so-called ϕ = 0° positioning mode (when the DAC axis lies in the diffraction plane) minimizes the DAC absorption and maximizes the access to the reciprocal-lattice nodes. The time required for measuring each reflection had to be extended considerably (usually by a factor of 5–10 compared to routine measurements carried out for bare crystals) because of the DAC absorption and high background of the radiation scattered on the beryllium discs, gasket and diamonds.

Several other DAC types, operating in both transmission and transverse geometries, were developed for the diffrac­tometer measurements (e.g. Denner et al., 1978), however the heavy cells required a sophisticated mounting on the diffractometer and often required difficult crystal-mounting and DAC-centring procedures.

4.2. CCD detector era

The development of two-dimensional electronic detectors for X-ray diffractometers soon prompted their use for high-pressure studies (Piltz et al., 1992; Shimomura et al., 1992; Allan et al., 2000; Shobu et al., 2001; Crichton & Mezouar, 2004; Ahsbahs, 2004). In several respects, the application of diffractometers equipped with a CCD camera considerably simplified the high-pressure experiments.

After initial difficulties with sample centring, a highly efficient automatic gasket-shadow method was developed (Budzianowski & Katrusiak, 2004; Angel, 2004; Dawson et al., 2004). The UB-matrix determination prior to the data collection is not necessary because the CCD camera records the diffraction images, which can be analysed after the experiment. The UB-matrix determination is easier when all the data are available. Owing to the two-dimensional detector, the data collection is much faster than by using the scintillation detector, and usually a considerable redundancy of the data is obtained. The redundancy of the data allows several important systematic errors to be eliminated by comparing reflection intensities, such as those caused by overlaid reflections from the sample and from the diamonds or ruby standards, by the primary and diffracted beams truncated on the DAC window edges, and by weakening of the beams by simultaneous diffraction events on the sample crystal and diamond anvils. Inspection of images is very helpful for verifying the intensities of outlier reflections. `Blind measurements' on new phases are possible when one is not certain if a new synthesized product or a new phase has been obtained, and the unit-cell and symmetry determination can all be performed after completing the data collection.

On the other hand, owing to the simultaneous recording of reflections and absence of one diffraction plane associated with the instrument, the reflections are not recorded precisely at the optimal DAC position. Approximately optimal DAC positioning can be obtained by maintaining the ϕ = 0° positioning mode (Budzianowski & Katrusiak, 2004), however this can be done only on four-circle diffractometers (three-axis crystal orienter plus the θ-axis detector positioner) made by several manufacturers. Meanwhile, CCD diffractometers with three axes only (ω axis and ϕ spindle at a fixed χ angle, and the detector axis) have become very common, but the completeness and quality of high-pressure data measured on such instruments is considerably lower.

4.3. High-pressure neutron diffraction studies

High-pressure neutron diffraction constitutes another branch of high-pressure crystallography, which appeared and developed during the last decades (McWhan, 1984; Bloch & Voiron, 1984; Voiron & Vettier, 1987; Miletich et al., 2000; Goncharenko, 2004; Somenkov, 2005). The neutron diffraction can provide significant complementary information in many structural problems, for example when protons have to be located precisely, when the structure investigated contains very heavy elements, when nuclei with a similar number of electrons have to be distinguished, when magnetic structures are investigated, and also for inelastic scattering experiments. The main difficulty in these experiments is a relatively low intensity of neutron sources, reactors or spallation sources, compared even to the intensity of the X-ray beam from conventional sealed tubes, not to mention synchrotrons, and the scattering of neutrons by most materials is low. Therefore the samples investigated by neutrons are much larger, usually single crystals of a few mm³ and powder samples of a few cm³ are used.

Several types of high-pressure cells for neutron diffraction studies have been built and are used both at nuclear reactors and at spallation sources. Generally, the cells for high-pressure neutron diffraction are large and in most cases adapted to varied-temperature environments. The main types of high-pressure cells for neutrons are (i) gas-pressure cells, (ii) cylinder-and-piston cells, and (iii) opposed-anvils cells. In the gas pressure cell, the pressure is generated by a compressor outside the `bomb' containing the sample and transmitted to it through a capillary (Paureau & Vettier, 1975); a pressure of about 0.5 GPa can be generated in these cells. The cylinder-and-piston cells are bigger and usually driven by a hydraulic press (Mizuki & Endoh, 1981; McWhan, 1984), but a higher pressure of about 3 GPa can be obtained. The walls of the gas or liquid pressure-cell bombs and the cylinders are made of materials that scatter neutrons weakly: aluminium alloys, vanadium, Ti₆₆Zr₃₄ alloy (having zero scattering amplitude due to the opposite signs of scattering amplitudes of Ti and Zr), and tungsten-carbide- or steel-supported Al₂O₃. The highest range of pressure is attainable in the opposed-anvils cells. Constructions of most of opposed-anvils cells for neutrons incorporate anvils with a recess in the centre to enclose a larger sample – so called Chechevitsa anvils (Stishov & Popova, 1961); or toroid anvils, with toroid grooves in the anvils around the sample space (Khvostantsev et al., 1977, 2004). The anvils are made of tungsten carbide, and of sapphire or diamond for higher-pressure ranges. Single-crystal neutron diffraction measurements in the pressure approaching 40 GPa were carried out (Glazkov et al., 1989), however the large diamond anvils used were prohibitively expensive. At present perhaps the most widely used is the so-called Paris–Edinburgh cell, based on opposed toroid anvils and optimized for time-of-flight neutron diffraction in pulsed neutron sources (Besson et al., 1992), but also applied at synchrotrons for experiments where the X-ray beam passes through the gasket. A DAC has been applie in neutron diffraction studies too (Goncharenko, 2006).