The equation of state of polyamorphic germania glass: A two‐domain description of the viscoelastic response

Optical full-field strain measurement within a diamond anvil cell

Digital image correlation computations are run on optical images of iron samples within a diamond anvil cell to obtain in-plane strain components at the surface of the sample up to 17 GPa. The α-Fe → ε-Fe transition onset pressure and phase coexistence pressure domain can be identified from the evolution of the surface average of strain components. Strain fields exhibit localizations for both direct and reverse transition; they coincide with the approximate boundary locations of reversion variants inside the microstructure of a single crystal sample. The so-called DICDAC (Digital Image Correlation within a Diamond Anvil Cell) setup is then a suitable tool for the investigation of phase transformations strains under pressure. In addition, specific volumes that are deduced from strain out of the transition pressure domains agree within ΔV/V = 0.4% with the equation of state data from the literature.

Liquid-Liquid Phase Transition in Metallic Droplets

We report theoretical evidence of the substrate-induced liquid-liquid phase transition (LLPT) behaviors in a single Al droplet and Ti-Al droplets. The Al droplet can produce an LLPT induced by substrates in part, forming a special three-layer structure. However, the introduction of a Ti droplet can promote the LLPT in an Al droplet. Al and Ti droplets do not coalesce into a homogeneously mixed droplet but produce the ordered liquid films. The substrate-induced LLPT in the Al droplet is characterized by the transition from the disordered to ordered structure. Results indicate that the substrate and the Ti droplet are the driving forces to promote the LLPT. The LLPT of the Ti-Al droplets in the wedge-shaped substrate is also observed, indicating that the confined Ti-Al droplets are more likely to undergo an LLPT.

Isothermal equation of state of crystalline and glassy materials from optical measurements in diamond anvil cells

Here, we present a method to study the equation of state of opaque amorphous and crystalline materials in diamond anvil cells. The approach is based on measurements of sample dimensions using high-resolution optical microscopy. Data on the volumetric strain as a function of pressure allow deriving the isothermal equation of state of the studied material. The analysis of optical images is fully automatized and allows measuring the sample dimensions with the precision of about 60 nm. The methodology was validated by studying isothermal compression of ω-Ti up to 30 GPa in a Ne pressure transmitting medium. Within the accuracy of the measurements, the bulk modulus of ω-Ti determined using optical microscopy was similar to that obtained from x-ray diffraction. For glassy carbon compressed to ∼30 GPa, the previously unknown bulk modulus was found to be equal to K₀ = 28 (2) GPa [K' = 5.5(5)].

Direct Volumetric Study of High-Pressure Driven Polyamorphism and Relaxation in the Glassy Germanium Chalcogenides

High precision measurements were taken of the specific volume of glassy germanium chalcogenides GeSe2, GeS2, Ge17Se83, and Ge8Se92 under hydrostatic pressure to 8.5 GPa. For GeSe2 and GeS2 glasses in the pressure range to 3 GPa the behavior is an elastic one with bulk modulus softening at pressures above 2 GPa. At higher pressures the relaxation processes begin that have logarithmic kinetics. The relaxation rate for GeSe2 glasses has a clearly pronounced maximum at 3.5-4.5 GPa, which is indicative of the existence of several mechanisms of structural transformations. For nonstoichiometric glasses inelastic behavior is observed at pressures above 1-1.5 GPa, the relaxation rate being much less than that for stoichiometric ones. For all the glasses we observe the "loss of memory" about the prehistory: A pressure rising after relaxation causes the return of values of the specific volume to the curve of compression without relaxation. After depressurization the residual densification makes up nearly 7% in stoichiometric glasses and 1.5% in Ge17Se83 glasses. The values of the effective bulk modulus for nonstoichiometric glasses coincide upon pressure lowering with the values after isobaric relaxations during pressure increase, whereas for GeSe2 the moduli during the decompression exceed substantially the values after isobaric relaxations at compression path. The results obtained demonstrate high capacity of the volumetric measurements to reveal the nature of the transformations in glassy germanium chalcogenides under compression.

Signature of a polyamorphic transition in the THz spectrum of vitreous GeO2

The THz spectrum of density fluctuations, S(Q, ω), of vitreous GeO2 at ambient temperature was measured by inelastic x-ray scattering from ambient pressure up to pressures well beyond that of the known α-quartz to rutile polyamorphic (PA) transition. We observe significant differences in the spectral shape measured below and above the PA transition, in particular, in the 30-80 meV range. Guided by first-principle lattice dynamics calculations, we interpret the changes in the phonon dispersion as the evolution from a quartz-like to a rutile-like coordination. Notably, such a crossover is accompanied by a cusp-like behavior in the pressure dependence of the elastic response of the system. Overall, the presented results highlight the complex fingerprint of PA phenomena on the high-frequency phonon dispersion.

Networks under pressure: the development of in situ high-pressure neutron diffraction for glassy and liquid materials

The pressure-driven collapse in the structure of network-forming materials will be considered in the gigapascal (GPa) regime, where the development of in situ high-pressure neutron diffraction has enabled this technique to obtain new structural information. The improvements to the neutron diffraction methodology are discussed, and the complementary nature of the results is illustrated by considering the pressure-driven structural transformations for several key network-forming materials that have also been investigated by using other experimental techniques such as x-ray diffraction, inelastic x-ray scattering, x-ray absorption spectroscopy and Raman spectroscopy. A starting point is provided by the pressure-driven network collapse of the prototypical network-forming oxide glasses B2O3, SiO2 and GeO2. Here, the combined results help to show that the coordination number of network-forming structural motifs in a wide range of glassy and liquid oxide materials can be rationalised in terms of the oxygen-packing fraction over an extensive pressure and temperature range. The pressure-driven network collapse of the prototypical chalcogenide glass GeSe2 is also considered where, as for the case of glassy GeO2, site-specific structural information is now available from the method of in situ high-pressure neutron diffraction with isotope substitution. The application of in situ high-pressure neutron diffraction to other structurally disordered network-forming materials is also summarised. In all of this work a key theme concerns the rich diversity in the mechanisms of network collapse, which drive the changes in physico-chemical properties of these materials. A more complete picture of the mechanisms is provided by molecular dynamics simulations using theoretical schemes that give a good account of the experimental results.

Mechanisms of network collapse in GeO2 glass: high-pressure neutron diffraction with isotope substitution as arbitrator of competing models

The structure of the network forming glass GeO(2) is investigated by making the first application of the method of in situ neutron diffraction with isotope substitution at pressures increasing from ambient to 8 GPa. Of the various models, the experimental results are in quantitative agreement only with molecular dynamics simulations made using interaction potentials that include dipole-polarization effects. When the reduced density ρ/ρ(0) > or approximately equal to 1.16, where ρ(0) is the value at ambient pressure, network collapse proceeds via an interplay between the predominance of distorted square pyramidal GeO(5) units versus octahedral GeO(6) units as they replace tetrahedral GeO(4) units. This replacement necessitates the formation of threefold coordinated oxygen atoms and leads to an increase with density in the number of small rings, where a preference is shown for sixfold rings when ρ/ρ(0) = 1 and fourfold rings when ρ/ρ(0) = 1.64.

Density-driven structural transformations in network forming glasses: a high-pressure neutron diffraction study of GeO2 glass up to 17.5 GPa

The structure of GeO(2) glass was investigated at pressures up to 17.5(5) GPa using in situ time-of-flight neutron diffraction with a Paris-Edinburgh press employing sintered diamond anvils. A new methodology and data correction procedure were developed, enabling a reliable measurement of structure factors that are largely free from diamond Bragg peaks. Calibration curves, which are important for neutron diffraction work on disordered materials, were constructed for pressure as a function of applied load for both single and double toroid anvil geometries. The diffraction data are compared to new molecular-dynamics simulations made using transferrable interaction potentials that include dipole-polarization effects. The results, when taken together with those from other experimental methods, are consistent with four densification mechanisms. The first, at pressures up to approximately equal 5 GPa, is associated with a reorganization of GeO(4) units. The second, extending over the range from approximately equal 5 to 10 GPa, corresponds to a regime where GeO(4) units are replaced predominantly by GeO(5) units. In the third, as the pressure increases beyond ~10 GPa, appreciable concentrations of GeO(6) units begin to form and there is a decrease in the rate of change of the intermediate-range order as measured by the pressure dependence of the position of the first sharp diffraction peak. In the fourth, at about 30 GPa, the transformation to a predominantly octahedral glass is achieved and further densification proceeds via compression of the Ge-O bonds. The observed changes in the measured diffraction patterns for GeO(2) occur at similar dimensionless number densities to those found for SiO(2), indicating similar densification mechanisms for both glasses. This implies a regime from about 15 to 24 GPa where SiO(4) units are replaced predominantly by SiO(5) units, and a regime beyond ~24 GPa where appreciable concentrations of SiO(6) units begin to form.

Determining the equation of state of amorphous solids at high pressure using optical microscopy

A method to determine the volumetric equation of state of amorphous solids using optical microscopy in a diamond anvil cell is described. The method relies on two- dimensional image acquisition and analysis to quantify changes in the projected image area with compression. The area analysis methods prove to be robust against improper focusing and lighting conditions while providing the accuracy necessary to deduce small area changes, which correspond to small volume changes in an isotropic material. The image capture, area analysis method is used to determine the compression of cubic crystals, yielding results in good agreement with diffraction and volumetric measurements. As a proof of concept, the equation of state of amorphous red phosphorus is measured up to 12 GPa under hydrostatic conditions where the quantified volume change between the red and black phases is approximately ΔV/V(0) ≈ 0.05 after a reduction of volume nearing 35% at 8 GPa. A large hysteresis is present during decompression and eventually results in a 15% permanent densification relative to the starting volume, which is attributed to a pressure induced crystallization from red to black phosphorus. The robustness of the technique is also demonstrated by measuring the equation of state of GeSe(2) glasses for semi transparent samples and As(2)O(3) in which gold coating is used as a contrasting aid.

High-pressure behaviour of GeO2: a simulation study

In this work we study the high-pressure behaviour of liquid and glassy GeO(2) by means of molecular dynamics simulations. The interaction potential, which includes dipole polarization effects, was parametrized using first-principles calculations. Our simulations reproduce the most recent experimental structural data very well. The character of the pressure-induced structural transition in the glassy system has been a matter of controversy. We show that our simulations and the experimental data are consistent with a smooth transition from a tetrahedral to an octahedral network with a significant number of pentacoordinated germanium ions appearing over an extended pressure range. Finally, the study of high-pressure, liquid germania confirms that this material presents an anomalous behaviour of the diffusivity as observed in analogous systems such as silica and water. The importance of pentacoordinated germanium ions for such behaviour is stressed.

Heterogeneities in confined water and protein hydration water

We report recent efforts to understand a broad range of experiments on confined water and protein hydration water, many initiated by a collaboration between workers at the University of Messina and MIT-the editors of this special issue. Preliminary calculations are not inconsistent with one tentative interpretation of these experiments as resulting from the system passing from the high-temperature high-pressure 'HDL' side of the Widom line (where the liquid might display non-Arrhenius behavior) to the low-temperature low-pressure 'LDL' side of the Widom line (where the liquid might display Arrhenius behavior). The Widom line-defined to be the line in the pressure-temperature plane where the correlation length has its maximum-arises if there is a critical point. Hence, interpreting the Messina-MIT experiments in terms of a Widom line is of potential relevance to testing, experimentally, the hypothesis that water displays a liquid-liquid critical point.

A new EXAFS investigation of local structural changes in amorphous and crystalline GeO(2) at high pressure

Structural transformations at high pressure in amorphous and quartz-like crystalline GeO(2) have been investigated by using a Paris-Edinburgh press coupled to EXAFS spectroscopy. From both the germanium absorption edge position and the Ge-O distance evolution, new detailed information has been obtained about the pressure behavior of the short range order. Crystalline GeO(2) undergoes a transformation from four- to six-fold coordination at about 8.5 GPa, but at least the whole 6-12 GPa pressure range should be considered as the transition region. On the other hand, amorphous GeO(2) is characterized by a much more gradual structural change and the full octahedral state is not reached at 13 GPa as commonly believed. Furthermore, no support to the recently claimed fully pentahedral intermediate state can be given. EXAFS signals of glassy GeO(2) beyond the first Ge-O shell qualitatively confirm the continuous breakdown of the intermediate range order up to 10 GPa.

Structural transition in compressed amorphous sulfur

Properties of amorphous sulfur (a-S) were investigated by synchrotron x-ray diffraction up to 100 GPa between 40 and 175 K. Measurements of the structure factor yielded the radial distribution function and the densities of two amorphous forms. a-S undergoes a structural transition above 65 GPa, accompanied by density discontinuity of 7%. These results indicate the amorphous-amorphous transition, from a low-density to a high-density form, and open up the possibility for the direct measurements of density of liquid-amorphous materials at extreme conditions.

Structure of glassy GeO2

The full set of partial structure factors for glassy germania, or GeO₂, were accurately measured by using the method of isotopic substitution in neutron diffraction in order to elucidate the nature of the pair correlations for this archetypal strong glass former. The results show that the basic tetrahedral Ge(O_1/2)₄ building blocks share corners with a mean inter-tetrahedral Ge-Ô-Ge bond angle of 132(2)°. The topological and chemical ordering in the resultant network displays two characteristic length scales at distances greater than the nearest neighbour. One of these describes the intermediate range order, and manifests itself by the appearance of a first sharp diffraction peak in the measured diffraction patterns at a scattering vector k_FSDP≈1.53 Å^-1, while the other describes so-called extended range order, and is associated with the principal peak at k_PP = 2.66(1) Å^-1. We find that there is an interplay between the relative importance of the ordering on these length scales for tetrahedral network forming glasses that is dominated by the extended range ordering with increasing glass fragility. The measured partial structure factors for glassy GeO₂ are used to reproduce the total structure factor measured by using high energy x-ray diffraction and the experimental results are also compared to those obtained by using classical and first principles molecular dynamics simulations.

Density measurements of noncrystalline materials at high pressure with diamond anvil cell

We describe an x-ray absorption method for in situ density measurement of non-crystalline materials in the diamond anvil cell using a monochromatic synchrotron x-ray microbeam. Sample thickness, which is indispensable in the absorption method, can be determined precisely by extrapolating the thickness profile of the gasket obtained by x-ray absorption and diffraction measurements. Diamond deformation across the sample chamber becomes noticeable at high pressures above 10 GPa, which can be monitored with a precision better than 1%, as demonstrated by measurements on crystalline Ag. We have applied the developed method to measure densities of the classic network-forming GeO(2) glass in octahedral form at pressures up to 56 GPa. The fit to the pressure-volume data with the Birch-Murnaghan equation from 13 to 56 GPa gives parameters of V(0)=23.2+/-0.4 cm(3)mol and K=35.8+/-3.0 GPa, assuming that K(')=4. This method could be applicable for in situ determination of the density of liquids and other noncrystalline materials using a diamond anvil cell up to ultrahigh pressures.

Distinct thermal behavior of GeO2 glass in tetrahedral, intermediate, and octahedral forms

One fascinating high-pressure behavior of tetrahedral glasses and melts is the local coordination change with increasing pressure, which provides a structural basis for understanding numerous anomalies in their high-pressure properties. Because the coordination change is often not retained upon decompression, studies must be conducted in situ. Previous in situ studies have revealed that the short-range order of tetrahedrally structured glasses and melts changes above a threshold pressure and gradually transforms to an octahedral form with further pressure increase. Here, we report a thermal effect associated with the coordination change at given pressures and show distinct thermal behaviors of GeO(2) glass in tetrahedral, octahedral, and their intermediate forms. An unusual thermally induced densification, as large as 16%, was observed on a GeO(2) glass at a pressure of 5.5 gigapascal (GPa), based on in situ density and x-ray diffraction measurements at simultaneously high pressures and high temperatures. The large thermal densification at high pressure was found to be associated with the 4- to 6-fold coordination increase. Experiments at other pressures show that the tetrahedral GeO(2) glass displayed small thermal densification at 3.3 GPa arising from the relaxation of intermediate range structure, whereas the octahedral glass at 12.3 GPa did not display any detectable thermal effects.

Anomalous compression behavior in lanthanum/cerium-based metallic glass under high pressure

In situ high-pressure x-ray diffraction, low-temperature resistivity, and magnetization experiments were performed on a La(32)Ce(32)Al(16)Ni(5)Cu(15) bulk metallic glass (BMG). A sudden change in compressibility at approximately 14 GPa and a rapid increase of resistivity at approximately 12 K were detected, whereas magnetic phase transformation and magnetic field dependence of the low-temperature resistivity do not occur at temperatures down to 4.2 K. An interaction between conduction electrons and the two-level systems is suggested to explain the temperature and field dependences of resistivity of the BMG alloy. Although the cause of the unusual change in compressibility at approximately 14 GPa is not clear, we believe that it could be linked with the unique electron structure of cerium in the amorphous matrix. An electronic phase transition in BMG alloys, most likely a second-order amorphous-to-amorphous phase transition, is suggested.

Phase behavior of attractive and repulsive ramp fluids: Integral equation and computer simulation studies

Using computer simulations and a thermodynamically self-consistent integral equation we investigate the phase behavior and thermodynamic anomalies of a fluid composed of spherical particles interacting via a two-scale ramp potential (a hard core plus a repulsive and an attractive ramp) and the corresponding purely repulsive model. Both simulation and integral equation results predict a liquid-liquid demixing when attractive forces are present, in addition to a gas-liquid transition. Furthermore, a fluid-solid transition emerges in the neighborhood of the liquid-liquid transition region, leading to a phase diagram with a somewhat complicated topology. This solidification at moderate densities is also present in the repulsive ramp fluid, but in this case inhibits the fluid-fluid separation.

Pressure-induced structural transformation in radiation-amorphized zircon

We study the response of a radiation-amorphized material to high pressure. We have used zircon ZrSiO4 amorphized by natural radiation over geologic times, and have measured its volume under high pressure, using the precise strain-gauge technique. On pressure increase, we observe apparent softening of the material, starting from 4 GPa. Using molecular dynamics simulation, we associate this softening with the amorphous-amorphous transformation accompanied by the increase of local coordination numbers. We observe permanent densification of the quenched sample and a nontrivial "pressure window" at high temperature. These features point to a new class of amorphous materials that show a response to pressure which is distinctly different from that of crystals.

Structure of liquid GeO2 from a computer simulation model

The structural properties of liquid GeO2 are investigated by means of molecular dynamics simulation using a pairwise potential. The simulations were performed in the microcanonical ensemble on systems with up to 576 particles prepared at 21 different densities, corresponding to pressures from -2 to 30 GPa, and temperatures of 1500 K and 3000 K. The pair correlation function, coordination number, angular distribution, and both the neutron and x-ray static structure factors are obtained and compared with those of liquid silica. The analysis of these results for the system at zero pressure indicates that in the liquid state the short range order is dominated by the presence of slightly distorted Ge(O(1/2))(4) tetrahedra. These tetrahedra are linked to each other mainly through the corners, with a Ge-O-Ge angle of approximately 130 degrees, similar to the amorphous phase. Beyond the basic tetrahedron some order persists, but to less extent than in liquid silica. Simulation of systems at higher densities shows a volume collapse in the pressure-volume curve in the range of 4-8 GPa, suggesting the possibility that a liquid-liquid phase transition occurs, as the one observed in the amorphous phase.

General view of a liquid-liquid phase transition

We present a general view of a liquid-liquid phase transition, based on a simple physical picture that there is "cooperative medium-range bond ordering" for any liquids. Contrary to the common belief, we argue that liquid is not homogeneous and in any liquid there exist locally favored structures, which are frustrated with normal-liquid structures. The cooperative excitation of locally favored structures leads to a gas-liquid-like critical point of bond ordering. This picture naturally leads to the conclusion that liquid-liquid transition is not specific to special materials, but can in principle exist in any liquids. Our model suggests a new possibility that (i) even an ordinary molecular liquid can have a hidden liquid-liquid phase transition and (ii) it may be the origin of a second amorphous phase (e.g., "glacial phase") and critical-like, large-scale fluctuations ("Fischer clusters") observed in supercooled molecular liquids.

First-order amorphous-amorphous transformation in silica

Molecular simulations predict that a first-order amorphous-amorphous transformation occurs in SiO2 under pressure, analogous to the first-order amorphous-amorphous transformation known to occur in H2O. At low temperatures the first-order transformation is kinetically hindered, and an amorphous-amorphous transformation occurs instead by gradual spinodal decomposition at higher pressures. We suggest that previous experiments have observed the spinodal decomposition pathway in SiO2 and that the predicted first-order transformation will be observed in experiments carried out at higher temperatures.