V. R. Belosludov

The mechanisms for pressure-induced amorphization of ice Ih

There has been considerable interest in the structure of liquid water at low temperatures and high pressure following the discovery of the high-density amorphous (HDA) phase of ice Ih (ref. 1). HDA ice forms at a pressure close to the extrapolated melting curve of ice, leading to the suggestion that it may have structure similar to that of dense water. On annealing, HDA ice transforms into a low-density amorphous (LDA) phase with a distinct phase boundary,. Extrapolation of thermodynamic data along the HDA–LDA coexistence line into the liquid region has led to the hypothesis that there might exist a second critical point for water and the speculation that liquid water is mixture of two distinct structures with different densities,. Here we critically examine this hypothesis. We use quasi-harmonic lattice-dynamics calculations to show that the amorphization mechanism in ice Ih changes from thermodynamic melting for T > 162 K to mechanical melting at lower temperatures. The vibrational spectra of ice Ih, LDA ice and quenched water also indicate a structure for LDA ice that differs from that of the liquid. These results call into question the validity of there being a thermodynamic connection between the amorphous and liquid phases of water.

The low frequency vibrations in clathrate hydrates

The mechanism for the unexpectedly strong interactions between the guest and lattice vibrations in clathrate hydrates is revealed from molecular dynamics and lattice dynamics calculations on model systems. It is shown that the vibrational couplings are the result of avoided crossings of the enclathrated guest localized rattling modes with the host lattice acoustic phonon branches of the same symmetry. Through these couplings, energy can be exchanged between the host lattice and the guest vibrations and lead to the anomalous glasslike behavior in the thermal conductivity of gas hydrates.

Theory of Clathrates

A review is presented of the theory of clathrate compounds, starting with the first quantitative theory suggested by van der Waals and Platteeuw and ending with the current ideas. A brief description is given of the theory of ideal and non-ideal solid clathrate solutions and of the theory allowing us to describe clathrates with an unstable, empty host lattice. The review is composed of results obtained by the different methods based on various approximations.In the concluding section predictions are made of the further development of the theory.

Elastic moduli and instability in molecular crystals

The phenomenon of instability in pressurized molecular crystals is studied using the lattice-dynamics approach. General expressions for the elastic moduli are obtained taking into account both short-range and long-range (electrostatic) interactions within the framework of the quasi-harmonic approximation. The behaviour of a system under changing pressure and temperature conditions and the Born stability criteria are investigated. Two types of instabilities, dynamical and thermodynamical, associated with the elastic moduli are presented. The dynamical instability occurs when the instability of acoustic modes of the phonon Hamiltonian occurs in the q = 0 region. The nature of thermodynamical stability implies that the equilibrium state of the crystal becomes thermodynamically unstable with respect to a small homogeneous deformation of the crystal lattice when the Born stability criteria are violated for isothermal or adiabatic moduli. These types of instabilities are illustrated in a series of calculations for ice Ic using the SPC potential for waters interactions. The results show that one of the stability conditions for the isothermal (adiabatic) moduli is violated at kbar and, as a consequence, thermodynamical instability occurs. In contrast, the dynamical instability of the phonon spectrum occurs at a significantly higher pressure, about 20 kbar.

Vibrational spectrum, elastic moduli and mechanical stability in ice VIII

The elastic moduli of ice VIII at different temperatures and pressures have been calculated from the quasiharmonic lattice dynamics method employing the TIP4P potential for water. It was found that under decompression, one of the Born’s stability conditions for solids was violated and ice VIII became mechanically unstable which led to a phase transformation. The transition pressure was found to decrease with temperature. This phenomenon is a symmetric equivalent of the pressure-induced crystal→amorphous transformation in ice Ih. Based on the theoretical results, it is proposed that the observed transformation of ice VIII to high density amorphous ice at low temperature is probably due to a mechanical instability in the crystal.

Theoretical modelling of the phase diagrams of clathrate hydrates for hydrogen storage applications

An original approach accounting for multiple cavity occupancy, host lattice relaxation and the description of the quantum nature of guest behaviour has been used for the estimation of the thermodynamic properties of pure hydrogen and binary C2H6 + H2 hydrates with the possibility of multiple filling of cavities by guest molecules. It has been found that the pure hydrogen cubic structure II (CS-II) hydrate is more thermodynamically stable than the cubic structure I (CS-I) hydrate in a wide range of p–T regions. However, at low pressure, the stabilisation of the CS-I hydrate can be realised for H2–C2H6–H2O systems even with small concentrations of ethane in the gas phase. However, in this case, the amount of stored hydrogen strongly depends on the ethane concentrations in the gas phase. At low concentration of ethane, the amount of hydrogen stored, 2.5 wt%, in CS-I hydrate can be achieved at T = 250 K. We believe that the present approach can be useful for understanding the thermodynamic properties of the binary hydrate and it can support the experimental exploration of novel hydrogen storage materials based on clathrate hydrates.

Mechanical Stability of Gas Hydrates under Pressure

When clathrate hydrates are compressed at high pressure, the crystalline structures collapse into high-density phases. The nature of the phase transition was postulated 1 to be related to the onset of mechanical instability by analogy with the amorphization of ice under pressure. However, unlike ice, the dense structures revert back to the original crystalline hydrate structures when allowed to recover at ambient pressure. This memory effect was observed experimentally at T = 77 K in Structure II THF and SF 6 clathrate hydrates, and was confirmed by molecular dynamics calculation for the Structure I ethylene oxide (EO) and Structure II Kr hydrates. 1 Furthermore, the volume–pressure behavior near the phase transition was found differ for hydrate with different enclathrated guests. For example, the experiments show a very sharp transition at P = 13 kbar for THF hydrate, a much smoother volume decrease at P = 15.8 kbar for SF 6 hydrate, and the absence of sudden volume change for Xe hydrate when compressed to 18 kbar. 1 In order to investigate the mechanism for this novel transformations, the quasiharmonic lattice dynamics method 2,3 and a new geometry optimization scheme for the accurate description of structural details, are used to compute elastic constants for the examination of the mechanical stability of clathrate hydrate with different arrangements of proton positions under compression. For comparison, methane and xenon hydrates and a hypothetical empty Structure I hydrate were investigated.

Dynamic and thermodynamic properties of clathrate hydrates

Vibrational spectra and thermodynamic properties of ices and the cubic structure I (CS-I) clathrate hydrate have been studied by the lattice dynamics method. The phonon density of states for the empty hydrate framework and for xenon hydrate have been determined; the vibrational frequencies of the guest molecules in large and small cavities have been found. The stability of the hydrate with respect to the external pressure at low temperatures and its thermodynamic stability at temperatures around 0°C have been studied. It has been found that the empty hydrate framework is unstable in certain temperature and pressure regions. A definite degree of occupation of the large cavities by the guest molecules is necessary for the hydrate to become stable. It has been found that there is a maximum of the critical temperature at which the hydrate exists, which is a function of the external pressure.

Hydroquinone clathrates and the theory of clathrate formation

The model of a clathrate solid solution, taking into account directed and nondirected guest-guest interactions, has been obtained using statistical thermodynamic methods in the approximation of the mean-field type for the general case (the formation of cavities of several types and the inclusion of different kinds of guest molecules by the host). Consideration of this interaction has been shown to improve the quantitative agreement between theory and experiment. When the guest-guest interaction is considerable in the case of guest molecules of the same type a phase transition (of a gas-liquid type) of the guest component may occur in the clathrate matrix. In the case of guests of two different types, the phase transition of the guest subsystem of the liquid-liquid type may also occur within one framework at the expense of a preferable interaction among guest molecules of the same type.We present the isothermal (20°C) section of the phase diagram of a hydroquinone-— formic acid — acetonitrile system. Clathrates, forming in the binary systems (with hydroquinone) produce restricted solid solutions (of type IV, according to Roozeboom). These and other experimental data are discussed in terms of the proposed theory.

Clathrate thermodynamics for the unstable host framework

We have introduced the concept of clathrates whose empty host framework is unstable. In contrast to the Van der Waals theory, according to which the empty host framework is metastable, we believe it to become metastable when, in the cellular clathrates, certain type of cavities are fully occupied or, in the channel clathrates, the guest molecules are closely packed. The free energy of the channel and cellular types of clathrates has been determined using statistical thermodynamics methods. The obtained chemical potentials allowed us to describe the equilibrium of the clathrate with the stable host α-phase and the gaseous guest phase. For the cellular clathrates the equations have been obtained determining the dependence of the degree of filling of small cavities upon temperature and the gaseous phase pressure. In the case of the channel clathrates the set of equations on the composition and parameter of the orientational ordering is found. These equations enable us to describe quantitatively compressed state of the guest molecules in the channel and to find temperatures of orientational ordering.