The Use of Quartz as an Internal Pressure Standard in High-Pressure Crystallography
01 Aug 1997-Journal of Applied Crystallography (International Union of Crystallography)-Vol. 30, Iss: 4, pp 461-466
TL;DR: The use of oriented quartz single crystals is proposed as an improved internal pressure standard for high-pressure single-crystal diffraction experiments in diamond-anvil cells in this article.
Abstract: The unit-cell parameters of quartz, SiO2, have been determined by single-crystal diffraction at 22 pressures to a maximum pressure of 8.9 GPa (at room temperature) with an average precision of 1 part in 9000. Pressure was determined by the measurement of the unit-cell volume of CaF2 fluorite included in the diamond-anvil pressure cell. The variation of quartz unit-cell parameters with pressure is described by: a −4.91300 (11) = −0.0468 (2) P + 0.00256 (7) P2 − 0.000094 (6) P3, c − 5.40482 (17) = − 0.03851 (2) P + 0.00305 (7) P2 − 0.000121 (6) P3, where P is in GPa and the cell parameters are in angstroms. The volume–pressure data of quartz are described by a Birch–Murnaghan third-order equation of state with parameters V0 = 112.981 (2) a3, KT0 = 37.12 (9) GPa and K′ = 5.99 (4). Refinement of K′′ in a fourth-order equation of state yielded a value not significantly different from the value implied by the third-order equation. The use of oriented quartz single crystals is proposed as an improved internal pressure standard for high-pressure single-crystal diffraction experiments in diamond-anvil cells. A measurement precision of 1 part in 10 000 in the volume of quartz leads to a precision in pressure measurement of 0.009 GPa at 9 GPa.
Citations
More filters
[...]
TL;DR: A detailed guide to the methods by which the parameters of EoS can be obtained from experimental compression data is presented in this article, along with a diagnostic tool for assessing the quality of the results.
Abstract: Diffraction experiments at high pressures provide measurement of the variation of the unit-cell parameters of the sample with pressure and thereby the variation of its volume (or equivalently its density) with pressure, and sometimes temperature. This last is known as the ‘Equation of State’ (EoS) of the material. It is the aim of this chapter to present a detailed guide to the methods by which the parameters of EoS can be obtained from experimental compression data, and the diagnostic tools by which the quality of the results can be assessed. The chapter concludes with a presentation of a method by which the uncertainties in EoS parameters can be predicted from the uncertainties in the measurements of pressure and temperature, thus allowing high-pressure diffraction experiments to be designed in advance to yield the required precision in results.
The variation of the volume of a solid with pressure is characterised by the bulk modulus, defined as K = − V ∂ P /∂ V . Measured equations of state are usually parameterized in terms of the values of the bulk modulus and its pressure derivatives, K′ = −∂ K /∂ P and K″ = −∂2 K /∂ P 2, evaluated at zero pressure. These zero-pressure (or, almost equivalent, the room-pressure values) are normally denoted by a subscript “0,” thus: K = − V (∂ P /∂ V ) P =0, K ′ = −(∂ K /∂ P ) P =0, and K ″ = −(∂2 K /∂ P 2) P =0. However, throughout this chapter a number of notational conventions are followed for ease of presentation. Unless specifically stated, the symbols K′ and K ″ (without subscript) refer to the zero-pressure values at ambient temperature, all references to bulk modulus, K …
620 citations
TL;DR: The behavior of a number of commonly used pressure media, including nitrogen, argon, 2-propanol, a 4:1 methanol-ethanol mixture, glycerol and various grades of silicone oil, has been examined by measuring the X-ray diffraction maxima from quartz single crystals loaded in a diamond-anvil cell with each of these pressure media in turn.
Abstract: The behavior of a number of commonly used pressure media, including nitrogen, argon, 2-propanol, a 4:1 methanol–ethanol mixture, glycerol and various grades of silicone oil, has been examined by measuring the X-ray diffraction maxima from quartz single crystals loaded in a diamond-anvil cell with each of these pressure media in turn. In all cases, the onset of non-hydrostatic stresses within the medium is detectable as the broadening of the rocking curves of X-ray diffraction peaks from the single crystals. The onset of broadening of the rocking curves of quartz is detected at ∼9.8 GPa in a 4:1 mixture of methanol and ethanol and at ∼4.2 GPa in 2-propanol, essentially at the same pressures as the previously reported hydrostatic limits determined by other techniques. Gigahertz ultrasonic interferometry was also used to detect the onset of the glass transition in 4:1 methanol–ethanol and 16:3:1 methanol–ethanol–water, which were observed to support shear waves above ∼9.2 and ∼10.5 GPa, respectively, at 0.8–1.2 GHz. By contrast, peak broadening is first detected at ∼3 GPa in nitrogen, ∼1.9 GPa in argon, ∼1.4 GPa in glycerol and ∼0.9 GPa in various grades of silicone oil. These pressures, which are significantly lower than hydrostatic limits quoted in the literature, should be considered as the practical maximum limits to the hydrostatic behavior of these pressure media at room temperature.
446 citations
Cites background or methods from "The Use of Quartz as an Internal Pr..."
...…advantage that it is readily available in gem-quality samples that have intrinsically sharp diffraction peaks, it is easy to handle, and it is elastically soft with a bulk modulus of 37.12 (9) GPa (Angel et al., 1997) making the peak positions and widths sensitive to small non-hydrostatic stresses....
[...]
...The algorithm used for centering diffraction peaks (Angel et al., 1997) is completed with a final step scan of the ! circle and the resulting profile is fitted with a constrained pair of pseudo-Voigt functions that represent the contribution of the K 1 and K 2 components of the X-ray spectrum…...
[...]
...Upon initial compression the diffraction peak widths remain constant within experimental uncertainties, and the unit-cell parameters determined from the diffraction peak positions follow the evolution previously reported for hydrostatic conditions (Angel et al., 1997)....
[...]
...In the remaining experiments, pressures were determined from the diffraction pattern of the quartz by using the hydrostatic calibration of its equation of state (Angel et al., 1997)....
[...]
TL;DR: An Excel macro to calculate mineral and rock physical properties at elevated pressure and temperature is presented in this paper, which includes an expandable database of physical parameters for 52 rock-forming minerals stable at high pressures and temperatures.
Abstract: [1] An Excel macro to calculate mineral and rock physical properties at elevated pressure and temperature is presented. The workbook includes an expandable database of physical parameters for 52 rock-forming minerals stable at high pressures and temperatures. For these minerals the elastic moduli, densities, seismic velocities, and H2O contents are calculated at any specified P and T conditions, using basic thermodynamic relationships and third-order finite strain theory. The mineral modes of suites of rocks are also specifiable, so that their predicted aggregate properties can be calculated using standard solid mixing theories. A suite of sample rock modes taken from the literature provides a useful starting point. The results of these calculations can be applied to a wide variety of geophysical questions including estimating the alteration of the oceanic crust and mantle; predicting the seismic velocities of lower-crustal xenoliths; estimating the effects of changes in mineralogy, pressure and temperature on buoyancy; and assessing the H2O content and mineralogy of subducted lithosphere from seismic observations.
285 citations
TL;DR: New areas of thermodynamic exploration of phase diagrams, polymorphism, transformations between different phases and cohesion forces, structure-property relations, and a deeper understanding of matter at the atomic scale in general are accessible with the high-pressure techniques in hand.
Abstract: Since the late 1950's, high-pressure structural studies have become increasingly frequent, following the inception of opposed-anvil cells, development of efficient diffractometric equipment (brighter radiation sources both in laboratories and in synchrotron facilities, highly efficient area detectors) and procedures (for crystal mounting, centring, pressure calibration, collecting and correcting data). Consequently, during the last decades, high-pressure crystallography has evolved into a powerful technique which can be routinely applied in laboratories and dedicated synchrotron and neutron facilities. The variation of pressure adds a new thermodynamic dimension to crystal-structure analyses, and extends the understanding of the solid state and materials in general. New areas of thermodynamic exploration of phase diagrams, polymorphism, transformations between different phases and cohesion forces, structure–property relations, and a deeper understanding of matter at the atomic scale in general are accessible with the high-pressure techniques in hand. A brief history, guidelines and requirements for performing high-pressure structural studies are outlined.
224 citations
Cites background from "The Use of Quartz as an Internal Pr..."
...Highsymmetry 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)....
[...]
TL;DR: The gasketed diamond-anvil cell has become the standard tool for the generation of high pressures over the last three decades and has been applied in a wide range of experimental studies such as Brillouin scattering (Whitfield et al. 1976), Raman spectroscopy (Sharma 1977, Sherman 1984), NMR measurements (Lee et al., 1987) and, of course X-ray diffraction.
Abstract: The development of apparatus to maintain materials at high hydrostatic pressure has been an active area of research for many years. From the pioneering work of Bridgman, during the early part of this century (Bridgman 1971), until the late 1960s, massive hydraulicly driven Bridgman-anvil and piston-cylinder devices dominated high-pressure science. Although there were later improvements in design, such as multi-anvil devices, it was not until the advent of the gasketed diamond-anvil cell, in the mid 1960s, that high-pressure studies were possible in non-specialized laboratories. Diamond has remarkable properties; not only is it the hardest known material it is also highly transparent to many ranges of electromagnetic radiation. Indeed incorporating these attributes, the gasketed diamond-anvil cell has become the standard tool for the generation of high pressures over the last three decades and has been applied in a wide range of experimental studies such as Brillouin scattering (Whitfield et al. 1976), Raman spectroscopy (Sharma 1977, Sherman 1984), NMR measurements (Lee et al. 1987) and, of course X-ray diffraction. It is this utility across a large range of science through physics, earth science and lately the life sciences that makes the development of the diamond-anvil cell as significant a revolution for measurement under non-ambient conditions in the physical sciences as that of the invention of the transistor to the whole sphere of electronics and computation.
Figure 1.
Assembly of the gasketed diamond-anvil cell: principle of pressure generation.
As with all successful designs, the principles upon which the gasketed diamond-anvil cell (Van Valkenburg 1964) operates are elegantly simple (Fig. 1). The sample is placed in a pressure chamber created between the flat parallel faces (culets) of two opposed diamond anvils and the hole penetrating a hardened metal foil (= the gasket). A pressure calibrant is placed beside the sample and the free volume within …
207 citations
References
More filters
Book•
01 Jan 1985
TL;DR: In this paper, the physical properties of crystals systematically in tensor notation are presented, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them.
Abstract: First published in 1957, this classic study has been reissued in a paperback version that includes an additional chapter bringing the material up to date. The author formulates the physical properties of crystals systematically in tensor notation, presenting tensor properties in terms of their common mathematical basis and the thermodynamic relations between them. The mathematical groundwork is laid in a discussion of tensors of the first and second ranks. Tensors of higher ranks and matrix methods are then introduced as natural developments of the theory. A similar pattern is followed in discussing thermodynamic and optical aspects.
8,520 citations
Book•
01 Jun 1983
169 citations