Artificial Ice Research Articles

Laboratory Investigation on Mechanical Behavior of Artificial Ice under Triaxial Compression

A series of triaxial compression tests on an artificial ice with strain rate of 1.67×10-4/s at-6°C are carried out to investigate the mechanical behavior of ice. The influence of confining pressure on deformation and strength characteristics of ice is analyzed based on the experimental results. The results show that the stress-strain behavior and the strength of ice changes with increasing pressure in two distinct phases.

Ice lubrication for moving heavy stones to the Forbidden City in 15th- and 16th-century China

Lubrication plays a crucial role in reducing friction for transporting heavy objects, from moving a 60-ton statue in ancient Egypt to relocating a 15,000-ton building in modern society. Although in China spoked wheels appeared ca. 1500 B.C., in the 15th and 16th centuries sliding sledges were still used in transporting huge stones to the Forbidden City in Beijing. We show that an ice lubrication technique of water-lubricated wood-on-ice sliding was used instead of the common ancient approaches, such as wood-on-wood sliding or the use of log rollers. The technique took full advantage of the natural properties of ice, such as sufficient hardness, flatness, and low friction with a water film. This ice-assisted movement is more efficient for such heavy-load and low-speed transportation necessary for the stones of the Forbidden City. The transportation of the huge stones provides an early example of ice lubrication and complements current studies of the high-speed regime relevant to competitive ice sports.

Amplified Inception of European Little Ice Age by Sea Ice–Ocean–Atmosphere Feedbacks

Abstract The inception of the Little Ice Age (~1400–1700 AD) is believed to have been driven by an interplay of external forcing and climate system internal variability. While the hemispheric signal seems to have been dominated by solar irradiance and volcanic eruptions, the understanding of mechanisms shaping the climate on a continental scale is less robust. In an ensemble of transient model simulations and a new type of sensitivity experiments with artificial sea ice growth, the authors identify a sea ice–ocean–atmosphere feedback mechanism that amplifies the Little Ice Age cooling in the North Atlantic–European region and produces the temperature pattern suggested by paleoclimatic reconstructions. Initiated by increasing negative forcing, the Arctic sea ice substantially expands at the beginning of the Little Ice Age. The excess of sea ice is exported to the subpolar North Atlantic, where it melts, thereby weakening convection of the ocean. Consequently, northward ocean heat transport is reduced, reinforcing the expansion of the sea ice and the cooling of the Northern Hemisphere. In the Nordic Seas, sea surface height anomalies cause the oceanic recirculation to strengthen at the expense of the warm Barents Sea inflow, thereby further reinforcing sea ice growth. The absent ocean–atmosphere heat flux in the Barents Sea results in an amplified cooling over Northern Europe. The positive nature of this feedback mechanism enables sea ice to remain in an expanded state for decades up to a century, favoring sustained cold periods over Europe such as the Little Ice Age. Support for the feedback mechanism comes from recent proxy reconstructions around the Nordic Seas.

Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin Film with Patterned Nanostructures

We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.

Chiral nature of magnetic monopoles in artificial spin ice

Micromagnetic properties of monopoles in artificial kagome spin ice systems are investigated using numerical simulations. We show that micromagnetics brings additional complexity into the physics of these monopoles that is, by essence, absent in spin models: in addition to a fractionalized classical magnetic charge, monopoles in the artificial kagome ice are chiral at remanence. Our simulations predict that the chirality of these monopoles can be controlled without altering their charge state. This chirality breaks the vertex symmetry and triggers a directional motion of the monopole under an applied magnetic field. Our results also show that the choice of the geometrical features of the lattice can be used to turn on and off this chirality, thus allowing the investigation of chiral and achiral monopoles.

Marine ice deformation experiments: an empirical validation of creep parameters

Marine ice is increasingly recognized as an important component of ice shelves in Antarctica. Because it mainly accretes in “weak” locations, it plays a crucial role in ice shelf stability. Little is known however on the rheology of this particular material (low salinity, no bubbles, specific fabrics). We present marine ice deformation experiments in unconfined uniaxial compression at −10 °C, −6 °C, and −3 °C. Generally, marine ice samples confirm the value of n = 3 for Glen's power law. It also appears to behave systematically “harder” than artificial or meteoric isotropic ice samples used in the past, in the studied stress condition. Bulk salinity does not seem to have a significant impact on the viscosity. All deformation curves compare well with a generalized empirical temperature/viscosity relationship. They represent the first experimental validation of the lower boundary of this rheological relationship recommended for use in modeling ice dynamics.

Linear field demagnetization of artificial magnetic square ice

We have studied experimentally the states formed in artificial square ice nanomagnet systems following demagnetisation in a rotating in-plane applied magnetic field that reduces to zero in a manner that is linear in time. The final states are found to be controlled via the system's lattice constant, which determines the strength of the magnetostatic interactions between the elements, as well as the field ramping rate. We understand these effects as a requirement that the system undergoes a sufficiently large number of active rotations within the critical field window in which elements may be reversed, such that the interactions are allowed to locally exert their influence if the ground state is to be approached. On the other hand, if quenched disorder is too strong when compared to the interaction strength, any close approach to the ground state is impossible. These results show that it is not necessary for there to be any ac component to the field amplitude that is applied to the system during demagnetisation, which is the method almost exclusively employed in field protocols reported to date. Furthermore, by optimising the parameters of our linear demagnetisation protocol, the largest field-generated ground state domains yet reported are found.

In-situ measurements of the low frequency dielectric permittivity of first-year Antarctic sea ice

Abstract Measurement of the low frequency dielectric permittivity of sea ice is an important step in developing microstructural models that will permit the calculation of other physical properties of sea ice. We report the adaptation of the technique of cross-borehole resistivity tomography to obtain in-situ measurements of the horizontal component of the permittivity of first year Antarctic sea ice. Results show features of the permittivity previously identified from measurements on laboratory grown artificial sea ice. Modeling of the measured permittivity curves allows estimates of physical parameters related to the conduction mechanisms in the ice to be made. Both e ∞ , the high frequency relative permittivity, and χ , the susceptibility of the Debye relaxation, appear to depend upon brine volume fraction, while the time constant of relaxation is consistent with values determined from previous studies. Empirical parameters representing the effect of space charge polarization show complicated relationships with temperature, salinity and brine volume fraction. There are also indications that differences in some of these parameters occur between columnar ice, observed to exist to a depth of about 1.1 m, and incorporated platelet ice below this depth.

Impeding effect of air bubbles on normal grain growth of ice

Normal grain growth experiments were performed using polycrystalline ice samples with and without air bubbles. The bubble-free polycrystalline ice was prepared by a special sample preparation technique that employed a phase change method. The ice samples with air bubbles were prepared from a mixture of ice powder and pure distilled water using conventional methods. The temperature dependencies of the rate of grain growth were measured in artificial polycrystalline ice samples with and without air bubbles. The average grain growth exponent n of the ice with bubbles was much greater than the theoretical value of 2, while that of bubble-free ice was close to 2. The activation energy for the grain boundary migration of bubble-free ice was 110–120 kJ mol−1, whereas that of the ice with bubbles was between 40 and 70 kJ mol−1. The observation of the microscopic images of samples and analyses of the evolution of bubble size distribution and location during grain growth revealed that small air bubbles are caught and swept by moving grain boundaries and a coalescence of bubbles occurs. This indicates that the slow grain boundary migration of ice with bubbles is controlled by the migration of air bubbles dragged by grain boundary migration.

Magnetic hysteresis of an artificial square ice studied by in-plane Bragg x-ray resonant magnetic scattering

We report X-ray resonant magnetic scattering studies of a Permalloy artificial square ice nanomagnet array, focussing on the field-driven evolution of the sum Σ and difference Δ signals of left and right handed circularly polarized synchrotron X-rays at different lateral positions in reciprocal space Qx. We used X-rays tuned to the Fe L3 resonance energy, with the scattering plane aligned along a principal symmetry axis of the array. Details of the specular Δ hysteresis curve are discussed, following the system magnetization from an initial demagnetized state. The periodic structure gives rise to distinct peaks at in-plane reciprocal Bragg positions, as shown by fitting Σ(Qx) to a model based on a simple unit cell structure. Diffraction order-dependent hysteresis in Δ is observed, indicative of the reordering of magnetization on the system's two interpenetrating sublattices, which markedly deviates from an ideal Ising picture under strong applied fields.

Permittivity of ice at radio frequencies: Part II. Artificial and natural polycrystalline ice

Abstract Precise knowledge of the absolute value and frequency dependence of the dielectric permittivity of ice is the basis for interpretation of radio echo sounding data on glaciers and ice sheets. However, in the range of radio-frequencies, data from direct measurements of the permittivity are sparse, and partially lacking uncertainty estimates. Here, we present new results for artificial and natural ice samples obtained by means of frequency-dependent measurements from 10 MHz to 1.5 GHz with a coaxial transmission line cell. Measurements on eight artificial ice samples grown from ultra-pure water within the cell yield a mean value for the real part of the relative permittivity of 3.18 ± 0.01 at − 20 °C. Sole evidence for dispersion is detected for frequencies below 10 MHz, possibly attributed to the Debye-type relaxation behavior. Investigation of the crystal orientation of the artificial ice samples reveals the c-axes to be predominantly parallel to the electric field inside the cell and allows to calculate a value representative for isotropic crystal orientation of 3.16 ± 0.01. Measurements on acid-doped artificial ice show a linear dependence of the real part with acidity with a gradient of (21.1 ± 3.9) [1/M]. The real part of the relative permittivity of natural firn and ice samples from a high Alpine glacier range from 2.02 at a density of 0.515 g/cm 3 to 3.08 at 0.875 g/cm 3 . Quasi-continuous measurements with the present setup on an alpine firn core are now possible, with resolution depending on the coaxial cell's length, for direct comparison with the established dielectric profiling method.

Permittivity of ice at radio frequencies: Part I. Coaxial transmission line cell

At radio-frequencies, measurements of the permittivity of ice are sparse and with unknown or large uncertainty. Coaxial transmission lines have been established for frequency-dependent permittivity determination for a broad variety of materials. Here we present a coaxial transmission line setup originally designed for soil samples, now adapted for measuring ice samples between 10 MHz and 1.5 GHz. Measured scattering parameters are assessed for artifacts against a forward calculation based on transmission line theory. A Debye-type relaxation function for the complex permittivity is assumed to obtain the permittivity of ice from the measured full set of four scattering parameters by means of a genetic optimization algorithm. The algorithm is successfully validated against quasi-analytical and iterative computation techniques with reference measurements of a low-loss Teflon standard. Based on the forward calculation and the Teflon standard, the total uncertainty for measuring the real part of the permittivity is estimated to be around 1%. Additional measurements of reference materials air, water, ethanol and methanol are used for validation. The real part of the permittivity of eight artificial pure ice samples is found frequency-independent between 10 MHz and 1.5 GHz at − 20 °C, with a mean value of 3.18 ± 0.01.

An Analytical Thermodynamic Approach to Friction of Rubber on Ice

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

Domain dynamics and fluctuations in artificial square ice at finite temperatures

The thermally driven formation and evolution of vertex domains is studied for square artificial spin ice. A self-consistent mean-field theory is used to show how domains of ground state ordering form spontaneously, and how these evolve in the presence of disorder. The role of fluctuations is studied using Monte Carlo simulations and analytical modelling. Domain wall dynamics are shown to be driven by a biasing of random fluctuations towards processes that shrink closed domains, and fluctuations within domains are shown to generate isolated small excitations, which may stabilize as the effective temperature is lowered. Domain dynamics and fluctuations are determined by interaction strengths, which are controlled by inter-element spacing. The role of interaction strength is studied via experiments and Monte Carlo simulations. Our mean-field model is applicable to ferroelectric ‘spin’ ice, and we show that features similar to those of magnetic spin ice can be expected, but with different characteristic temperatures and rates.

Multi-step ordering in kagome and square artificial spin ice

We show that in colloidal models of artificial kagome and modified square ice systems, a variety of ordering and disordering regimes occurs as a function of the biasing field, temperature and colloid–colloid interaction strength, including ordered monopole crystals, biased ice rule states, thermally induced ice-rule ground states, biased triple states and disordered states. We describe the lattice geometries and biasing field protocols that create the different states and explain the formation of the states in terms of sublattice switching thresholds. For a system prepared in a monopole lattice state, we show that a sequence of different orderings occurs for increasing temperature. Our results also explain several features observed in nanomagnetic artificial ice systems under an applied field.

Thermodynamics of elementary excitations in artificial magnetic square ice

We investigate the thermodynamics of artificial square spin ice systems assuming only dipolar interactions among the islands that compose the array. Emphasis is given to the effects of temperature on elementary excitations (magnetic monopoles and their strings). By using Monte Carlo techniques we calculate the specific heat, the density of poles and their average separation as functions of temperature. The specific heat and average separation between monopoles with opposite charges exhibit a sharp peak and a local maximum, respectively, at the same temperature, Tp ≈ 7.2D/kB (here, D is the strength of the dipolar interaction and kB the Boltzmann constant). When the lattice size is increased, the amplitude of these features also increases but very slowly. Really, the specific heat and the maximum of the average separation dmax between oppositely charged monopoles increase logarithmically with system size, indicating that completely isolated charges could be found only at the thermodynamic limit. In general, the results obtained here suggest that, for temperatures T ⩾ Tp, these systems may exhibit a phase with separated monopoles, although the quantity dmax should not be larger than a few lattice spacings for viable artificial materials.

Towards a method for high vertical resolution measurements of the partial pressure of CO2 within bulk sea ice

AbstractFluxes of atmospheric CO2 have been reported over sea ice during winter and spring. These fluxes are partly driven by the gradient of the CO2 concentration between sea ice and the atmosphere. We present a new non-destructive method to measure the pCO2 of bulk sea ice at its in situ temperature. This method is based on an equilibration procedure between sea ice and a standard gas of known CO2 concentration. The concentration is measured by gas chromatography with a precision of 5%. Tests were performed on artificial standard sea ice and confirmed the reproducibility of the technique in the range of precision of the gas chromatograph. To test the accuracy of this method, the first profiles of pCO2 measured in bulk sea ice are reported and compared with direct in situ measurements of brine pCO2 over depth-integrated intervals.

Temporal evolution of surface and grain boundary area in artificial ice beads and implications for snow chemistry

Temporal evolution of surface and grain boundary area in artificial ice beads and implications for snow chemistry

3-D imaging and quantification of graupel porosity by synchrotron-based micro-tomography

Abstract. The air bubble structure is an important parameter to determine the radiation properties of graupel and hailstones. For 3-D imaging of this structure at micron resolution, a cryo-stage was developed. This stage was used at the tomography beamline of the Swiss Light Source (SLS) synchrotron facility. The cryo-stage setup provides for the first time 3-D-data on the individual pore morphology of ice particles down to infrared wavelength resolution. In the present study, both sub-mm size natural and artificial ice particles rimed in a wind tunnel were investigated. In the natural rimed ice particles, Y-shaped air-filled closed pores were found. When kept for half an hour at −8 °C, this morphology transformed into smaller and more rounded voids well known from literature. Therefore, these round structures seem to represent an artificial rather than in situ pore structure, in contrast to the observed y-shaped structures found in the natural ice particles. Hence, for morphological studies on natural ice samples, special care must be taken to minimize any thermal cycling between sampling and measurement, with least artifact production at liquid nitrogen temperatures.

Reducing Disorder in Artificial Kagome Ice

Artificial spin ice has become a valuable tool for understanding magnetic interactions on a microscopic level. The strength in the approach lies in the ability of a synthetic array of nanoscale magnets to mimic crystalline materials, composed of atomic magnetic moments. Unfortunately, these nanoscale magnets, patterned from metal alloys, can show substantial variation in relevant quantities such as the coercive field, with deviations up to 16%. By carefully studying the reversal process of artificial kagome ice, we can directly measure the distribution of coercivities, and, by switching from disconnected islands to a connected structure, we find that the coercivity distribution can achieve a deviation of only 3.3%. These narrow deviations should allow the observation of behavior that mimics canonical spin-ice materials more closely.