This critical review will be of interest to the experts in porous solids (including catalysis), but also solid state chemists and physicists. It presents the state-of-the-art on hybrid porous solids, their advantages, their new routes of synthesis, the structural concepts useful for their ‘design’, aiming at reaching very large pores. Their dynamic properties and the possibility of predicting their structure are described. The large tunability of the pore size leads to unprecedented properties and applications. They concern adsorption of species, storage and delivery and the physical properties of the dense phases. (323 references)

Hybrid porous solids: past, present, future

The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.

An internally consistent thermodynamic data set for phases of petrological interest

/pdf/metal-organic-frameworks-and-self-assembled-supramolecular-2xs948xxr9.pdf

Metal–Organic Frameworks and Self-Assembled Supramolecular Coordination Complexes: Comparing and Contrasting the Design, Synthesis, and Functionality of Metal–Organic Materials

The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral-fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order-disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha-beta quartz transition to be handled more satisfactorily. Several melt end- members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data. kinetics which apply to determining directly the greatest majority of such equilibria in the laboratory, for forming solid solutions, and inclusion of aqueous and silicate melt species), and provides uncertainties especially at lower temperatures, as well as the diYculty of establishing reversals of reactions involving solid allowing the likely uncertainties on the results of thermodynamic calculations to be estimated. This is a solutions. The levels of precision and accuracy required of thermodynamic data in order to be able to forward- critical issue in that calculations using data sets should always involve uncertainty propagation to help evalu- model synthetic and natural mineral assemblages mean that the continuing upgrading and expansion of the ate the results. Because the experimental phase equilib- ria involve overlapping subsets of compositional space, data set by incorporation of new phase equilibrium constraints, calorimetry and new measurements of the derived thermodynamic data are highly correlated, and it is only the inclusion of the correlations which molar volume, thermal expansion and compressibility are more than justified. enables the reliable calculation of uncertainties on mineral reactions to be performed. Earlier work on mineral thermodynamic data sets for rock-forming minerals includes compilations of The thermodynamic data extraction involves using weighted least squares on the diVerent types of data

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Properties Of Concrete

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 …

Equations of State

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.

Effective hydrostatic limits of pressure media for high-pressure crystallographic studies

The relationship between linear elasticity theo- ry of solids and their equations of state (EoS) is reviewed, along with the commonly-used types of isothermal EoS, thermal expansion models, and P-V-T EoS. A new con- sole program, EosFit7c, is presented. It performs EoS cal- culations and fitting for both volume and linear isother- mal data, isobaric data and P-T data. Linear data is handled by cubing the quantities and treating them as volumes in all EoS formulations. Least-squares fitting of EoS to data incorporates the option to weight the fit with the measurement uncertainties in P, V and T simulta- neously. The EosFit7c program is built with a new library of subroutines for EoS calculations and manipulation, written in Fortran. The library has been incorporated as a module, cfml_eos, in the publicly-available CrysFML li- brary. The module handles Murnaghan, Tait, Birch-Mur- naghan, Vinet, and Natural Strain EoS. For P-V-T calcula- tions any of these isothermal EoS can be combined with a variety of published thermal expansion models, includ- ing a model of thermal pressure. The entire library has been revalidated against other software and against an ab-initio re-derivation of the EoS, which identified a number of small errors in published formulae for some EoS.

/pdf/eosfit7c-and-a-fortran-module-library-for-equation-of-state-23lqby5rgt.pdf

EosFit7c and a Fortran module (library) for equation of state calculations

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.

/pdf/the-use-of-quartz-as-an-internal-pressure-standard-in-high-4cqcxauwcv.pdf

The Use of Quartz as an Internal Pressure Standard in High-Pressure Crystallography

Two superconducting phases, ${\mathrm{Tl}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10+\mathrm{\ensuremath{\delta}}}$ (2223) and ${\mathrm{Tl}}_{2}$${\mathrm{Ca}}_{1}$${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{2}$${)}_{8+\mathrm{\ensuremath{\delta}}}$ (2122), both with onset ${\mathrm{T}}_{\mathrm{c}}$ near 120 K and zero resistivity at 100 K, have been isolated from samples in the Tl-Ca-Ba-Cu-O system. The new 2223 superconductor has a 5.40\ifmmode\times\else\texttimes\fi{}5.40\ifmmode\times\else\texttimes\fi{}36.25-A${\mathrm{\r{}}}^{3}$ pseudotetragonal unit cell. The 2122 superconductor, which appears to be structurally related to ${\mathrm{Bi}}_{2}$${\mathrm{CaSr}}_{2}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$, has a 5.44\ifmmode\times\else\texttimes\fi{}5.44\ifmmode\times\else\texttimes\fi{}29.55-A${\mathrm{\r{}}}^{3}$ pseudotetragonal subcell. The 2223 phase is probably related to 2122 by the addition of extra calcium and copper layers.

Ross J. Angel

Papers

Equations of State

Effective hydrostatic limits of pressure media for high-pressure crystallographic studies

EosFit7c and a Fortran module (library) for equation of state calculations

The Use of Quartz as an Internal Pressure Standard in High-Pressure Crystallography

100-K superconducting phases in the Tl-Ca-Ba-Cu-O system.