Residual entropy of ice nanotubes and ice layers

A relatively simple algorithm is presented for the complete enumeration of all H-bond networks in finite fragments of ice nanotubes and ice layers with periodic boundary conditions. This algorithm is based on the well-known transfer matrix method and it includes a convenient procedure for calculation of the elements of transfer matrices themselves. To facilitate this, it is necessary to specify only very small local matrices of sizes 2×2 or 4×4. We present exhaustive statistics of H-bonds arrangements for finite-size zigzag- and armchair-like ice nanotubes, for the fragments of hexagonal monolayer and bilayer and also for ice nanotubes consisting of stacked n$n$-membered rings. Using the new algorithm, we have also calculated the specific residual entropy for the infinite two-dimensional lattices. The agreement with the well-known solution for a square ice model demonstrates the reliability of the obtained results.     

The Effects of Charge Transfer Interactions on the Properties of Ice Ih

Potential models which include charge transfer are used to study ice/water coexistence properties and properties of the ice Ih phase. Two charge transfer models are used, one which is non-polarizable and one which is polarizable. These models transfer a discreet amount of charge for each hydrogen bond made and the net charge of a molecule is determined by the difference in the number of hydrogen bonds a molecule makes as a donor and as an acceptor. In ice Ih, this difference is very near zero and the net amount of charge transfer is correspondingly essentially zero. This differs from the amount of charge transfer in the liquid phase. The results for the polarizable charge transfer model confirm other studies that suggest the importance of polarizability in reproducing the high dielectric constant of ice Ih.     

Neutron scattering studies of structural transformations and vibrational spectra of ice after high pressure treatment

Abstract

The transitions of the recovered high-pressure phase ice VIII first to high-density amorphous (hda) and low-density amorphous ices, and finally to cubic Ic, and hexagonal Ih ice were observed at heating using real-time neutron diffraction. Inelastic incoherent neutron scattering measurements on the hdu ice, ice Ih and high-pressure phase ice VI revealed similarity between the amorphous phase and crystalline ice VI and led to the new proposition that hda ice consists of two interpenetrating hydrogen-bounded networks with no hydrogen bonds between “sublattices”.     

Anomalous behavior of proton zero point motion in water confined in carbon nanotubes

The momentum distribution of the protons in ice Ih, ice VI, high density amorphous ice, and water in carbon nanotubes has been measured using deep inelastic neutron scattering. We find that at 5 K the kinetic energy of the protons is 35 meV less than that in ice Ih at the same temperature, and the high momentum tail of the distribution, characteristic of the molecular covalent bond, is not present. We observe a phase transition between 230 and 268 K to a phase that does resemble ice Ih. Although there is yet no model for water that explains the low temperature momentum distribution, our data reveal that the protons in the hydrogen bonds are coherently delocalized and that the low temperature phase is a qualitatively new phase of ice.     

Multicanonical sampling of the space of states of ℋ(2, <Emphasis Type="Italic">n</Emphasis>)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.     

Phonon dispersion of ice under pressure

We report measurements of the phonon dispersion of ice Ih under hydrostatic pressure up to 0.5 GPa, at 140 K, using inelastic neutron scattering. They reveal a pronounced softening of various low-energy modes, in particular, those of the transverse acoustic phonon branch in the [100] direction and polarization in the hexagonal plane. We demonstrate with the aid of a lattice dynamical model that these anomalous features in the phonon dispersion are at the origin of the negative thermal expansion (NTE) coefficient in ice below 60 K. Moreover, extrapolation to higher pressures shows that the mode frequencies responsible for the NTE approach zero at approximately 2.5 GPa, which explains the known pressure-induced amorphization (PIA) in ice. These results give the first clear experimental evidence that PIA in ice is due to a lattice instability, i.e., mechanical melting.     

Reciprocity principle for radiative transfer models that use periodic boundary conditions

Many numerical models use periodic boundary conditions in solving the radiative transfer through heterogeneous media specified over a fixed domain. A reciprocity principle applicable to solutions from these models is derived for the common situation of a scattering and absorbing heterogeneous medium that is illuminated over the entire domain from a single direction. The derived reciprocity principle states that the domain-averaged bidirectional reflectance distribution function remains invariant when incoming and outgoing directions are interchanged, regardless of the heterogeneity of the medium and the size of the domain. This reciprocity principle provides a simple and useful benchmark test for radiative transfer models that use periodic boundary conditions.     

Theoretical investigation of structures,compositions, and phase transitions of neon hydrates based on ices Ih and II

Thermodynamic conditions of existence in the p-T plane and the composition of neon hydrates based on ices Ih and II are determined. The occupancy of neon in cages (channels) of ices Ih and II at temperatures below 0°C is calculated. It is shown that the occupancy of neon in hydrate based on ices cages decreases with growing temperature. Lines of monovariant equilibria between gas phase (neon)-neon hydrate based on ice Ih-liquid water (or ice II) and neon-gas phase (neon)-hydrate based on ice II-liquidwater (or ice II) are found. The line of divariant equilibria between neon hydrate based on ice Ih-neon hydrate based on ice II has been also calculated. The possibility of ice stabilization due to inclusion of neon into ice cages (channels) is shown.     

基于六角形和球形冰晶模型的卷云辐射特征研究

卷云中冰晶粒子的单次光散射计算是卷云辐射传输及云微物理参数反演的重要基础。近年,利用高观测频率的静止气象卫星数据来反演水云和卷云的光学和微物理参数,进而计算地表光通量的研究倍受重视。然而,很多研究中卷云的冰晶用球形模型来模拟。由于不同形状和尺度大小的冰晶对电磁波的散射特征的不同,导致不同冰晶模型计算的卷云环境下卫星观测的辐射值及地表光通量的不同。利用不同尺度大小和电磁波波长的球形和六角形冰晶的单次散射数据,结合RSTAR辐射传输模式来定量分析了卷云环境下不同形状的冰晶模型对计算卫星观测的辐射和地表光通量中的影响。结果显示利用不同形状的冰晶模块来计算的卫星观测的辐射,地表向下辐射通量明显不同。波长在0.4～1.0 μm之间的大气窗口部分的光谱辐射通量的差距最大。总辐射通量受云粒子形状的影响显著。研究证实了正确选择冰晶模型对卫星反演卷云微物理和光学参数的反演及计算地表光通量的重要性。该结果对于云微物理参数的反演及地表向下辐射通量的模拟具有参考价值。     

Ground-state properties of crystalline ice from periodic hartree-fock calculations and a coupled-cluster-based many-body decomposition of the correlation energy

Ground state properties of crystalline ice Ih are investigated by combining periodic Hartree-Fock calculations with a many-body expansion for the electron correlation energy using second-order many-body perturbation theory and coupled-cluster techniques. Very good agreement with experimental data can already be achieved by considering two-body correlation contributions up to the third coordination shell in crystalline ice. This hints at the possibility to accurately simulate ab initio water by using periodic Hartree-Fock calculations together with a parametrized two-body correlation potential.     

A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.     

Anomalous Diffusion in a Model with a Variable Percolation Radius

Anomalous diffusion models for random 1-D cluster and comb structures of length L = 100 with finite fingers and different boundary conditions are considered. The effect of electric field on anomalous diffusion is discussed. The cases with different percolation radii are compared. The comb-structure model with periodic boundary conditions is shown to be useful in studying various types of anomalous diffusion. A new diffusion type, where the average rate is higher than the typical rate, is predicted. Physical causes for this diffusion are revealed.     

Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy

We use boundary weights and reflection equations to obtain families of commuting double-row transfer matrices for interaction-round-a-face models with fixed boundary conditions. In particular, we consider the fusion hierarchy of the Andrews-Baxter-Forrester (ABF) models, for which we obtain diagonal, elliptic solutions to the reflection equations, and find that the double-row transfer matrices satisfy functional equations with the same form as in the case of periodic boundary conditions.     

SH-wave propagation and scattering in periodically layered composites with a damaged layer

Plane SH-wave propagation in periodically layered elastic composites with a damaged layer is investigated. Two different models are developed to approximate the damaged layer, namely, a periodic array of cracks and continuously distributed springs in the layer. In the first model, the total wave field in the elastic stack of layers with cracks is described as a sum of incident wave field modeled by the transfer matrix method and the scattered wave field governed by an integral representation in terms of the crack-opening-displacements on the crack-faces. The integral equation derived from the boundary conditions on the crack-faces is solved numerically by a Galerkin method. By using Bloch–Floquet theorem the crack-opening-displacements for a periodic array of cracks are expressed by the crack-opening-displacement on a reference crack. In the spring model, the spring constant is estimated by the material properties and the crack density and the modified transfer matrix method is used to compute the wave reflection and transmission coefficients. Numerical results obtained by both models are presented and discussed. Special attention of the analysis is devoted to wave transmissions and reflections, band gaps, wave localization and resonance phenomena due to damages. The influences of the damage types (periodic cracks and stochastic cracks approximated by distributed springs) on the wave field pattern and the band gaps are analyzed.     

The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states

We present a rigorous study of the classical ground-states under boundary conditions of a class of one-dimensional models generalizing the discrete Frenkel-Kontorova model. The extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic, quasi-periodic and chaotic orbits. For all boundary conditions, we select among all the extremum solutions of the energy of the model, those which correspond to the ground-states of the infinite system. We prove that these ground-states are either periodic (commensurate) or quasi-periodic (incommensurate) but are never chaotic. We also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions. The topological structure of the whole set of ground-states is described in details. In addition to physical applications, consequences for twist map homeomorphisms are mentioned. Part II (S. Aubry, P.Y. LeDaeron and G. Andre) will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map.     

A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus

Absorption and extinction properties of the finite hexagonal ice column and hexagonal ice plate in random and preferred orientation are studied at the wavelength of 80 μm using a new implementation of exact T-matrix theory. For the case of random orientation at size parameters around two, it is shown that the hexagonal ice column and hexagonal ice plate absorption resonances are diminished relative to Mie theory, and the same behaviour is also noted for an aggregate particle consisting of eight hexagonal elements. The absorption properties of the aggregate particle have been calculated using the finite-difference time-domain method. It is also shown that extinction and absorption solutions for the hexagonal ice column and hexagonal ice plate can differ significantly if incidence occurs perpendicular or parallel to the cylindrical axis of the hexagon. For the case of perpendicular incidence on the edge of the hexagon, absorption solutions can exceed those of Mie theory, and for the case of parallel incidence, behaviour of the extinction solutions for hexagonal ice columns and hexagonal ice plates is shown to be similar to previously published work based on the prolate and oblate spheroid. Interference structure, associated with surface waves, is resolved on the hexagonal column extinction solution and the hexagonal plate absorption solution, thereby demonstrating that surface waves can exist on a non-axisymmetric geometry. The usefulness of assuming the hexagonal ice column in retrieval of ice crystal effective size is also investigated using aircraft based radiometric observations of semi-transparent cirrus at the wavelengths of 8.5 and 11 μm.     

等效球模型模拟冰晶云反射的误差分析

用射线光学理论计算了具有一定尺度分布的六角冰晶粒子在可见和近红外光谱区一系列波长上(0.2～5μm)的单次散射特性.利用米氏(Mie)理论,计算了与六角冰晶具有相同截面积的球形粒子的单次散射特性.根据辐射传输理论,应用累加法,分别计算了由冰晶粒子和等效球形粒子构成的卷层云的多次散射特性,计算结果表明当入射波长λ≈3.0 μm时,等效球Mie理论可以很好地用于计算卷层云的反射特性,但是当λ＜2.8μm时,尤其在可见光区,将引起显著的误差.最后提出了计算冰云光学特性的两种方案.     

Anomalous pressure-induced transition(s) in ice XI

The effects of pressure on the structure of ice XI-an ordered form of the phase of ice Ih, which is known to amorphize under pressure-are investigated theoretically using density-functional theory. We find that pressure induces a mechanical instability, which is initiated by the softening of an acoustic phonon occurring at an incommensurate wavelength, followed by the collapse of the entire acoustic band and by the violation of the Born stability criteria. It is argued that phonon collapse may be a quite general feature of pressure-induced amorphization. The implications of our findings for the amorphization of ice Ih are also discussed.     

A 3D implementation of ray tracing combined with diffraction on facets: Verification and a potential application

A 3D implementation of a new model of light scattering applicable to dielectric faceted objects is introduced. The model combines standard geometric optics with diffraction on individual facets. It can be applied to any faceted geometry. The model adds no significant computational overheads to classical geometric optics yet provides much improved results. Initial results for long hexagonal columns are compared to SVM and appear favourable. 2D scattering patterns are calculated for a hexagonal column in a fixed orientation and compared to those created by ice analogue crystals in the laboratory with close agreement. The comparison includes the observation of a guided wave propagating along the length of the column. The new model is then applied to a selection of geometries to illustrate how it could be used to aid particle characterization, particularly in the case of cirrus ice.     

Physical and Mechanical Behavior of Ice Under Dynamic Loading

Russian Physics Journal - The physical and mechanical behavior of ice is studied by the example of the Ih ice phase using the method of numerical simulation in a computational model of damaged...