Accurate and precise lattice parameters of H2O and D2O ice Ihbetween 1.6 and 270 K from high-resolution time-of-flight neutron powder diffraction data

Ice formation and its elimination in cryopreservation of oocytes

Damage from ice and potential toxicity of ice-inhibiting cryoprotective agents (CPAs) are key issues in assisted reproduction of humans, domestic and research animals, and endangered species using cryopreserved oocytes and embryos. The nature of ice formed in bovine oocytes (similar in size to oocytes of humans and most other mammals) after rapid cooling and during rapid warming was examined using synchrotron-based time-resolved x-ray diffraction. Using cooling rates, warming rates and CPA concentrations of current practice, oocytes show no ice after cooling but always develop large ice fractions-consistent with crystallization of most free water-during warming, so most ice-related damage must occur during warming. The detailed behavior of ice at warming depended on the nature of ice formed during cooling. Increasing cooling rates allows oocytes soaked as in current practice to remain essentially ice free during both cooling and warming. Much larger convective warming rates are demonstrated and will allow routine ice-free cryopreservation with smaller CPA concentrations. These results clarify the roles of cooling, warming, and CPA concentration in generating ice in oocytes and establish the structure and grain size of ice formed. Ice formation can be eliminated as a factor affecting post-warming oocyte viability and development in many species, improving outcomes and allowing other deleterious effects of the cryopreservation cycle to be independently studied.

Thermophysical properties of H2O and D2O ice Ih with contributions from proton disorder, quenching, relaxation, and extended defects: A model case for solids with quenching and relaxation

Application of the coherent thermodynamic model [W. Holzapfel and S. Klotz, J. Chem. Phys. 155, 024506 (2021)] for H2O ice Ih to the more detailed data for D2O ice Ih provides better insight into the contributions from quenched proton disorder and offers a new basis for understanding the apparent differences between the data for thermal expansion measured with neutron diffraction on polycrystalline samples [A. Fortes, Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. 74, 196 (2018) and A. Fortes, Phys. Chem. Chem. Phys 21, 8264 (2019)] and macroscopic dilatation measurements on single crystals [D. Buckingham et al., Phys. Rev. Lett. 121, 185505 (2018)]. The comparison points to contributions from defects effecting the two techniques in different ways. The uncertainties in thermodynamic data due to the contributions from proton disorder and additional defects are compared with the "reference data" [R. Feistel and W. Wagner, J. Phys. Chem. Ref. Data 35, 1021 (2006)] for H2O ice Ih.

Ice formation and its elimination in cryopreservation of bovine oocytes

Damage from ice and potential toxicity of ice-inhibiting cryoprotective agents (CPAs) are key issues in assisted reproduction using cryopreserved oocytes and embryos. We use synchrotron-based time-resolved x-ray diffraction and tools from protein cryocrystallography to characterize ice formation within bovine oocytes after cooling at rates between ∼1000 °C/min and ∼600,000°C /min and during warming at rates between 20,000 and 150,000 °C /min. Maximum crystalline ice diffraction intensity, maximum ice volume, and maximum ice grain size are always observed during warming. All decrease with increasing CPA concentration, consistent with the decreasing free water fraction. With the cooling rates, warming rates and CPA concentrations of current practice, oocytes may show no ice after cooling but always develop substantial ice fractions on warming, and modestly reducing CPA concentrations causes substantial ice to form during cooling. With much larger cooling and warming rates achieved using cryocrystallography tools, oocytes soaked as in current practice remain essentially ice free during both cooling and warming, and when soaked in half-strength CPA solution oocytes remain ice free after cooling and develop small grain ice during warming. These results clarify the roles of cooling, warming, and CPA concentration in generating ice in oocytes, establish the character of ice formed, and suggest that substantial further improvements in warming rates are feasible. Ice formation can be eliminated as a factor affecting post-thaw oocyte viability and development, allowing other deleterious effects of the cryopreservation cycle to be studied, and osmotic stress and CPA toxicity reduced.

Significance Statement

Cryopreservation of oocytes and embryos is critical in assisted reproduction of humans and domestic animals and in preservation of endangered species. Success rates are limited by damage from crystalline ice, toxicity of cryoprotective agents (CPAs), and damage from osmotic stress. Time-resolved x-ray diffraction of bovine oocytes shows that ice forms much more readily during warming than during cooling, that maximum ice fractions always occur during warming, and that the tools and large CPA concentrations of current protocols can at best only prevent ice formation during cooling. Using tools from cryocrystallography that give dramatically larger cooling and warming rates, ice formation can be completely eliminated and required CPA concentrations substantially reduced, expanding the scope for species-specific optimization of post-thaw reproductive outcomes.

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H₂O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

Water adsorption and dynamics on graphene and other 2D materials: Computational and experimental advances

The interaction of water and surfaces, at molecular level, is of critical importance for understanding processes such as corrosion, friction, catalysis and mass transport. The significant literature on interactions with single crystal metal surfaces should not obscure unknowns in the unique behaviour of ice and the complex relationships between adsorption, diffusion and long-range inter-molecular interactions. Even less is known about the atomic-scale behaviour of water on novel, non-metallic interfaces, in particular on graphene and other 2D materials. In this manuscript, we review recent progress in the characterisation of water adsorption on 2D materials, with a focus on the nano-material graphene and graphitic nanostructures; materials which are of paramount importance for separation technologies, electrochemistry and catalysis, to name a few. The adsorption of water on graphene has also become one of the benchmark systems for modern computational methods, in particular dispersion-corrected density functional theory (DFT). We then review recent experimental and theoretical advances in studying the single-molecular motion of water at surfaces, with a special emphasis on scattering approaches as they allow an unparalleled window of observation to water surface motion, including diffusion, vibration and self-assembly.

Ab initio simulations of α- and β-ammonium carbamate (NH4·NH2CO2), and the thermal expansivity of deuterated α-ammonium carbamate from 4.2 to 180 K by neutron powder diffraction

Experimental and computational studies of ammonium carbamate have been carried out, with the objective of studying the elastic anisotropy of the framework manifested in (i) the thermal expansion and (ii) the compressibility; furthermore, the relative thermodynamic stability of the two known polymorphs has been evaluated computationally. Using high-resolution neutron powder diffraction data, the crystal structure of α-ammonium carbamate (ND4·ND2CO2) has been refined [space group Pbca, Z = 8, with a = 17.05189 (15), b = 6.43531 (7), c = 6.68093 (7) Å and V = 733.126 (9) Å3 at 4.2 K] and the thermal expansivity of α-ammonium carbamate has been measured over the temperature range 4.2-180 K. The expansivity shows a high degree of anisotropy, with the b axis most expandable. The ab initio computational studies were carried out on the α- and β-polymorphs of ammonium carbamate using density functional theory. Fitting equations of state to the P(V) points of the simulations (run athermally) gave the following values: V0 = 744 (2) Å3 and bulk modulus K0 = 16.5 (4) GPa for the α-polymorph, and V0 = 713.6 (5) Å3 and K0 = 24.4 (4) GPa for the β-polymorph. The simulations show good agreement with the thermoelastic behaviour of α-ammonium carbamate. Both phases show a high-degree of anisotropy; in particular, α-ammonium carbamate shows unusual compressive behaviour, being determined to have negative linear compressibility (NLC) along its a axis above 5 GPa. The thermodynamically stable phase at ambient pressure is the α-polymorph, with a calculated enthalpy difference with respect to the β-polymorph of 0.399 kJ mol-1; a transition to the β-polymorph could occur at ∼0.4 GPa.

Adsorption of C2-C5 alcohols on ice. A grand canonical Monte Carlo simulation study

In this paper, we report Grand Canonical Monte Carlo simulations performed to characterize the adsorption of four linear alcohol molecules, comprising between 2 and 5 carbon atoms (namely, ethanol, n-propanol, n-butanol, and n-pentanol) on crystalline ice in a temperature range typical of the Earth's troposphere.The adsorption details analysed at 228 K show that, at low coverage of the ice surface, the polar head of the adsorbed molecules tend to optimize its hydrogen bonding with the surrounding water, whereas the aliphatic chain lie more or less parallel to the ice surface. With increasing coverage, the lateral interactions between the adsorbed alcohol molecules lead to the reorientation of the aliphatic chains which tend to become perpendicular to the surface, the adsorbed molecules pointing thus their terminal methyl group up to the gas phase. When compared to the experimental data, the simulated and measured isotherms show a very good agreement, although a small temperature shift between simulations and experiments could be inferred from simulations at various temperatures. In addition, this agreement appears to be better for ethanol and n-propanol than for n-butanol and n-pentanol, especially at the highest pressures investigated, pointing to a possible slight underestimation of the lateral interactions between the largest alcohol molecules by the interaction potential model used. Nevertheless, the global accuracy of the approach used, as tested in tropospheric conditions, opens the way for its use in modeling studies also relevant to another (e.g., astrophysical) context.

On the role of intermolecular vibrational motions for ice polymorphs. III. Mode characteristics associated with negative thermal expansion

Low-pressure ice forms, such as hexagonal and cubic ice, expand on cooling below temperature 60 K. This negative thermal expansivity has been explored in terms of phonon frequency modulation with varying volume and attributed to the negative Grüneisen parameters unique mostly to tetrahedrally coordinated substances. However, an underlying mechanism for the negative Grüneisen parameters has not been known except some schematic analyses. We investigate in this study the characteristics of the intermolecular vibrational modes whose Grüneisen parameters are negative by examining the individual vibrational modes rigorously. It is found that the low frequency modes below 100 cm^-1, which we explicitly show are mostly bending motions of three hydrogen-bonded molecules, necessarily accompany elongation of the hydrogen bond length at peak amplitudes compared with that at the equilibrium position in executing the vibrational motions. The elongation gives rise to a decrease in the repulsive interaction while an increase in the Coulombic one. The decrease in the repulsive interaction is relaxed substantially by expansion due to its steep slope against molecular separation compared with the sluggish increase in the Coulombic one, and therefore, the negative Grüneisen parameters are obtainable. This scenario is tested against some variants of cubic ice with various water potential models. It is demonstrated that four interaction-site models are suitable to describe the intermolecular vibrations and the thermal expansivity because of the moderate tendency to favor the tetrahedral coordination.

The microscopic origin of the anomalous isotopic properties of ice relies on the strong quantum anharmonic regime of atomic vibration

Water ice is a unique material presenting intriguing physical properties, such as negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation to investigate how thermal and quantum fluctuations affect the physical properties of ice XI with ab initio accuracy. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: When progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume first expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low-energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first-principles and the simulation of ice under pressure.

Laboratory exploration of mineral precipitates from Europa's subsurface ocean

The precipitation of hydrated phases from a chondrite-like Na-Mg-Ca-SO4-Cl solution is studied using in situ synchrotron X-ray powder diffraction, under rapid- (360 K h-1, T = 250-80 K, t = 3 h) and ultra-slow-freezing (0.3 K day-1, T = 273-245 K, t = 242 days) conditions. The precipitation sequence under slow cooling initially follows the predictions of equilibrium thermodynamics models. However, after ∼50 days at 245 K, the formation of the highly hydrated sulfate phase Na2Mg(SO4)2·16H2O, a relatively recent discovery in the Na2Mg(SO4)2-H2O system, was observed. Rapid freezing, on the other hand, produced an assemblage of multiple phases which formed within a very short timescale (≤4 min, ΔT = 2 K) and, although remaining present throughout, varied in their relative proportions with decreasing temperature. Mirabilite and meridianiite were the major phases, with pentahydrite, epsomite, hydrohalite, gypsum, blödite, konyaite and loweite also observed. Na2Mg(SO4)2·16H2O was again found to be present and increased in proportion relative to other phases as the temperature decreased. The results are discussed in relation to possible implications for life on Europa and application to other icy ocean worlds.

Coherent thermodynamic model for ice Ih-A model case for complex behavior

New data on the variation of the thermal expansion of ice Ih with temperature at ambient pressure together with new evaluations of the bulk modulus and earlier data for the heat capacity provide the basis for a coherent thermodynamic modeling of the main thermophysical properties of ice Ih over its whole range of stability. The quasi-harmonic approximation with one Debye term and seven Einstein terms, together with explicit anharmonicity, represents the dominant contribution next to minor "anomalies" from hydrogen ordering and lattice defects. The model accurately fits the main features of all experimental data and provides a basis for the comparison with earlier determinations of the phonon density of states and the Grüneisen parameters.

Structure of the electrical double layer at the ice-water interface

The surface of ice in contact with water contains sites that undergo deprotonation and protonation and can act as adsorption sites for aqueous ions. Therefore, an electrical double layer should form at this interface and existing models for describing the electrical double layer at metal oxide-water interfaces should be able to be modified to describe the surface charge, surface potential, and ionic occupancy at the ice-water interface. I used a surface complexation model along with literature measurements of the zeta potential of ice in brines of various strength and pH to constrain equilibrium constants. I then made predictions of ion site occupancy, surface charge density, and partitioning of counterions between the Stern and diffuse layers. The equilibrium constant for cation adsorption is more than 5 orders of magnitude larger than the other constants, indicating that this reaction dominates even at low salinity. Deprotonated OH sites are predicted to be slightly more abundant than dangling O sites, consistent with previous work. Surface charge densities are on the order of ±0.001 C/m² and are always negative at the moderate pH values of interest to atmospheric and geophysical applications (6-9). In this pH range, over 99% of the counterions are contained in the Stern layer. This suggests that diffuse layer polarization will not occur because the ionic concentrations in the diffuse layer are nearly identical to those in the bulk electrolyte and that electrical conduction and polarization in the Stern layer will be negligible due to reduced ion mobility.

Ice in biomolecular cryocrystallography

Diffraction data acquired from cryocooled protein crystals often include diffraction from ice. Analysis of ice diffraction from crystals of three proteins shows that the ice formed within solvent cavities during rapid cooling is comprised of a stacking-disordered mixture of hexagonal and cubic planes, with the cubic plane fraction increasing with increasing cryoprotectant concentration and increasing cooling rate. Building on the work of Thorn and coworkers [Thorn et al. (2017), Acta Cryst. D73, 729-727], a revised metric is defined for detecting ice from deposited protein structure-factor data, and this metric is validated using full-frame diffraction data from the Integrated Resource for Reproducibility in Macromolecular Crystallography. Using this revised metric and improved algorithms, an analysis of structure-factor data from a random sample of 89 827 PDB entries collected at cryogenic temperatures indicates that roughly 16% show evidence of ice contamination, and that this fraction increases with increasing solvent content and maximum solvent-cavity size. By examining the ice diffraction-peak positions at which structure-factor perturbations are observed, it is found that roughly 25% of crystals exhibit ice with primarily hexagonal character, indicating that inadequate cooling rates and/or cryoprotectant concentrations were used, while the remaining 75% show ice with a stacking-disordered or cubic character.

Structural characterization of ice XIX as the second polymorph related to ice VI

Ice polymorphs usually appear as hydrogen disorder-order pairs. Ice VI has a wide range of thermodynamic stability and exists in the interior of Earth and icy moons. Our previous work suggested ice β-XV as a second polymorph deriving from disordered ice VI, in addition to ice XV. Here we report thermal and structural characterization of the previously inaccessible deuterated polymorph using ex situ calorimetry and high-resolution neutron powder diffraction. Ice β-XV, now called ice XIX, is shown to be partially antiferroelectrically ordered and crystallising in a √2×√2×1 supercell. Our powder data recorded at subambient pressure fit best to the structural model in space group [Formula: see text]. Key to the synthesis of deuterated ice XIX is the use of a DCl-doped D₂O/H₂O mixture, where the small H₂O fraction enhances ice XIX nucleation kinetics. In addition, we observe the transition from ice XIX to its sibling ice XV upon heating, which proceeds via a transition state (ice VI^‡) containing a disordered H-sublattice. To the best of our knowledge this represents the first order-order transition known in ice physics.

Simulation of Inelastic Neutron Scattering Spectra Directly from Molecular Dynamics Trajectories

Inelastic neutron scattering (INS) is a widely used technique to study atomic and molecular vibrations. With the increasing complexity of materials and thus the INS spectra, being able to simulate the spectra from various atomistic models becomes an essential step and also a major bottleneck for INS data analysis. The conventional approach using density functional theory and lattice dynamics often falls short when the materials of interest are complex (e.g., defective, disordered, heterogeneous, amorphous, large-scale), for which molecular dynamics driven by an interatomic force field is a more common approach. In this paper, we demonstrate a method to directly convert molecular dynamics trajectories into simulated INS spectra, including not only fundamental but also higher order excitations. The results are compared with data collected on various representative samples from different neutron spectrometers. This development will open great opportunities by providing the key tool to perform in-depth analysis of INS data and to validate and optimize computer models.

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

Calorimetric studies on ice II reveal a surprising H2O/D2O isotope effect. While the ice II to ice Ic transition is endothermic for H2O, it is exothermic for D2O samples. The transition enthalpies are +40 and -140 J/mol, respectively, where such a sign change upon isotope substitution is unprecedented in ice research. To understand the observations we employ force field calculations using two water models known to perform well for H2O ice phases and their vibrational properties. These simulations reveal that the isotope effect can be traced back to zero-point energy. q-TIP4P/F fares better and is able to account for approximately three-fourths of the isotope effect, while MB-pol only catches approximately one-third. Phonon and configurational entropy contributions are necessary to predict reasonable transition enthalpies, but they do not have an impact on the isotope effect. We suggest to use these calorimetric isotope data as a benchmark for water models.

The crystallography of Pluto

Maynard-Casely and co-workers [IUCrJ (2020). 7, 844-851.] investigate two of Pluto's most abundant minerals with neutron diffraction. The new results will be key to understanding the geology of our distant neighbour and represent a significant advance in the emerging field of small-molecule geology.

On the crystal structures and phase transitions of hydrates in the binary dimethyl sulfoxide–water system

Neutron powder diffraction data have been collected from a series of flash-frozen aqueous solutions of dimethyl sulfoxide (DMSO) with concentrations between 25 and 66.7 mol% DMSO. These reveal the existence of three stoichiometric hydrates, which crystallize on warming between 175 and 195 K. DMSO trihydrate crystallizes in the monoclinic space group P21/c, with unit-cell parameters at 195 K of a = 10.26619 (3), b = 7.01113 (2), c = 10.06897 (3) Å, β = 101.5030 (2)° and V = 710.183 (3) Å3 (Z = 4). Two of the symmetry-inequivalent water molecules form a sheet of tiled four- and eight-sided rings; the DMSO molecules are sandwiched between these sheets and linked along the b axis by the third water molecule to generate water–DMSO–water tapes. Two different polymorphs of DMSO dihydrate have been identified. The α phase is monoclinic (space group P21/c), with unit-cell parameters at 175 K of a = 6.30304 (4), b = 9.05700 (5), c = 11.22013 (7) Å, β = 105.9691 (4)° and V = 615.802 (4) Å3 (Z = 4). Its structure contains water–DMSO–water chains, but these are polymerized in such a manner as to form sheets of reniform eight-sided rings, with the methyl groups extending on either side of the sheet. On warming above 198 K, α-DMSO·2H2O undergoes a solid-state transformation to a mixture of DMSO·3H2O + anhydrous DMSO, and there is then a stable eutectic between these two phases at ∼203 K. The β-phase of DMSO dihydrate has been observed in a rapidly frozen eutectic melt and in very DMSO-rich mixtures. It is observed to be unstable with respect to the α-phase; above ∼180 K, β-DMSO·2H2O converts irreversibly to α-DMSO·2H2O. At 175 K, the lattice parameters of β-DMSO·2H2O are a = 6.17448 (10), b = 11.61635 (16), c = 8.66530 (12) Å, β = 101.663 (1)° and V = 608.684 (10) Å3 (Z = 4), hence this polymorph is just 1.16% denser than the α-phase under identical conditions. Like the other two hydrates, the space group appears likely, on the basis of systematic absences, to be P21/c, but the structure has not yet been determined. Our results reconcile 60 years of contradictory interpretations of the phase relations in the binary DMSO–water system, particularly between mole fractions of 0.25–0.50, and confirm empirical and theoretical studies of the liquid structure around the eutectic composition (33.33 mol% DMSO).

Cubic ice Ic without stacking defects obtained from ice XVII

Amongst the more than 18 different forms of water ice, only the common hexagonal phase and the cubic phase are present in nature on Earth. Nonetheless, it is now widely recognized that all samples of 'cubic ice' discovered so far do not have a fully cubic crystal structure but instead are stacking-disordered forms of ice I (namely, ice Isd), which contain both hexagonal and cubic stacking sequences of hydrogen-bonded water molecules. Here, we describe a method to obtain large quantities of cubic ice Ic with high structural purity. Cubic ice Ic is formed by heating a powder of D₂O ice XVII obtained from annealing of pristine C₀ hydrate samples under dynamic vacuum. Neutron diffraction experiments performed on two different instruments and Raman spectroscopy measurements confirm the structural purity of the cubic ice, Ic. These findings contribute to a better understanding of ice I polymorphism and the existence of the two natural ice forms.

On the role of intermolecular vibrational motions for ice polymorphs I: Volumetric properties of crystalline and amorphous ices

Intermolecular vibrations and volumetric properties are investigated using the quasiharmonic approximation with the TIP4P/2005, TIP4P/Ice, and SPC/E potential models for most of the known crystalline and amorphous ice forms that have hydrogen-disordering. The ice forms examined here cover low pressure ices (hexagonal and cubic ice I, XVI, and hypothetical dtc ice), medium pressure ices (III, IV, V, VI, XII, hydrogen-disordered variant of ice II), and high pressure ice (VII) as well as the low density and the high density amorphous forms. We focus on the thermal expansivities and the isothermal compressibilities in the low temperature regime over a wide range of pressures calculated via the intermolecular vibrational free energies. Negative thermal expansivity appears only in the low pressure ice forms. The sign of the thermal expansivity is elucidated in terms of the mode Grüneisen parameters of the low frequency intermolecular vibrational motions. Although the band structure for the low frequency region of the vibrational density of state in the medium pressure ice has a close resemblance to that in the low pressure ice, its response against volume variation is opposite. We reveal that the mixing of translational and rotational motions in the low frequency modes plays a crucial role in the appearance of the negative thermal expansivity in the low pressure ice forms. The medium pressure ices can be further divided into two groups in terms of the hydrogen-bond network flexibility, which is manifested in the properties on the molecular rearrangement against volume variation, notably the isothermal compressibility.

Structural manifestation of partial proton ordering and defect mobility in ice Ih

High precision lattice-parameter measurements provide a potential roadmap to producing partially-ordered states of water ice.

Quantum nature of the hydrogen bond from ambient conditions down to ultra-low temperatures

Quantum simulations reveal strong temperature effects for weak hydrogen bonds and differences in quantum delocalization between various hydrogen-bonded systems.

Thermal Expansion of Single-Crystal H_{2}O and D_{2}O Ice Ih

Thermal expansion of H_{2}O and D_{2}O ice Ih with relative resolution of 1 ppb is reported. A large transition in the thermal expansion coefficient at 101 K in H_{2}O moves to 125 K in D_{2}O, revealing one of the largest-known isotope effects. Rotational oscillatory modes that couple poorly to phonons, i.e., lattice solitons, may be responsible.

H/D isotope effect on the molar volume and thermal expansion of benzene

Time-of-flight neutron powder diffraction data have been collected from C₆H₆ and C₆D₆ between 10 and 276 K, revealing no cross-over in their molar volumes and an almost temperature invariant volume-isotope-effect, in contrast with previously published work.