Transport properties of supercooled confined water

This article presents an overview of recent experiments performed on transport properties of water in the deeply supercooled region, a temperature region of fundamental importance in the science of water. We report data of nuclear magnetic resonance, quasi-elastic neutron scattering, Fourier-transform infrared spectroscopy, and Raman spectroscopy, studying water confined in nanometer-scale environments. When contained within small pores, water does not crystallise, and can be supercooled well below its homogeneous nucleation temperature T_h. On this basis it is possible to carry out a careful analysis of the well known thermodynamical anomalies of water. Studying the temperature and pressure dependencies of water dynamics, we show that the liquid-liquid phase transition (LLPT) hypothesis represents a reliable model for describing liquid water. In this model, water in the liquid state is a mixture of two different local structures, characterised by different densities, namely the low density liquid (LDL) and the high-density liquid (HDL). The LLPT line should terminate at a special transition point: a low-T liquid-liquid critical point. We discuss the following experimental findings on liquid water: (i) a crossover from non-Arrhenius behaviour at high T to Arrhenius behaviour at low T in transport parameters; (ii) a breakdown of the Stokes-Einstein relation; (iii) the existence of a Widom line, which is the locus of points corresponding to maximum correlation length in the p-T phase diagram and which ends in the liquid-liquid critical point; (iv) the direct observation of the LDL phase; (v) a minimum in the density at approximately 70 K below the temperature of the density maximum. In our opinion these results represent the experimental proofs of the validity of the LLPT hypothesis.     

Spatial heterogeneity in liquid–liquid phase transition

Molecular dynamics simulations are performed to investigate the liquid–liquid phase transition(LLPT) and the spatial heterogeneity in Al–Pb monotectic alloys. The results reveal that homogeneous liquid Al–Pb alloy undergoes an LLPT,separating into Al-rich and Pb-rich domains, which is quite different from the isocompositional liquid water with a transition between low-density liquid(LDL) and high-density liquid(HDL). With spatial heterogeneity becoming large, LLPT takes place correspondingly. The relationship between the cooling rate, relaxation temperature and percentage of Al and the spatial heterogeneity is also reported. This study may throw light on the relationship between the structure heterogeneity and LLPT, which provides novel strategies to control the microstructures in the fabrication of the material with high performance.     

Pressure–temperature studies on conductivity of TlX(X=Cl,Br,I) compounds:: I: phase diagram. II: ionic mobility

We have measured the conductivity σ of TlX(X=Cl, Br, I) compounds up to 5.3 GPa and between 300–823 K. The σ–T dependence for all compounds can be divided into three distinct regions: (i) low temperature (LT), <400 K, with unusual negative σ–T dependence, (ii) intermediate temperature (IT), 400<650 K, with positive σ–T dependence and (iii) high temperature (HT), T>650 K, with positive σ–T dependence. The σ–T isobars were used to construct the T–P solid phase diagram for each compound. The LT region data indicate a new meta-stable phase in the 1.0–3.5 GPa range. The LT→IT transition is characterized by an inverse σ–T dependence followed by normal Arrhenius behavior up to and including the HT region. The extrapolation to 1 atm of the P-dependent boundary between IT and HT regions above 3 GPa for each compound in the P–T plot yields a value close to its respective normal (1 atm) T_melt suggesting a solid order–disorder transition type paralleling -AgI behavior. The abrupt drop in conductivity in the LT region for P between 2.5–4.1 GPa of all compounds is at variance with the Arrhenius behavior observed for unperturbed ion migration implying the appearance of a second factor overriding the Arrhenius temperature dependence. Normal Arrhenius σ–T dependence prevails in both IT and HT regions with Q_c values of 85–100 kJ mol⁻¹ and 50–75 kJ mol⁻¹, respectively. The higher conductivities at 0.4 GPa for TlBr and TlI relative to their 1 atm data and the increasing σ with P are in strong contrast to the normal σ-P behavior of TlCl. The dependence of activation volume ΔV^‡ on T for TlCl, i.e. ΔV^‡>0, shows abnormally high values with a maximum at 500 K for P<3.0 GPa but reasonable ΔV^‡ values appear above 3.0 GPa. The ΔV^‡–T dependence for both TlBr and TlI with ΔV^‡<0 is incompatible with an ion transport mechanism suggesting an electronic conduction process and implying an ionic–metallic transition at higher pressures. These contrasting conductivity features are discussed and interpreted in terms of electronegativity differences and bonding character rather than structure.     

Geometrical approach to the thermodynamical theory of phase transitions of the second kind

A geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure P and variable temperature T is proposed. Equilibrium states of a system at zero external field and fixed P and T are described by points in three-dimensional space with coordinates η, the order parameter, T, the temperature and /gf, the thermodynamic potential. These points form the so-called zero field curve in the (η, T, /gf) space. Its branch point coincides with the critical point of the system. The small parameter of the theory (the distance from the critical point along the zero-field curve) is shown to be more convenient than the small parameter of the Landau theory. It is emphasized that no explicit functional dependency of /gf on η and T is imposed.

It is shown that using (η, T, /gf) space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on η and T, but also on near (local) order parameters λ_i. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature T_c.     

Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C

The magnetization of single-crystal HoNi₂B₂C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi₂B₂C is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho⁺³ magnetic moments lie predominately in the tetragonal a−b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of T_N=5.0 K. Remarkably, in 20 Oe applied field both superconductivity (T_c=8.0 K) and antiferromagnetism (T_N=5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H−T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of H_c2 with a deep minimum at T_N=5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T < 5 K and H < 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi₂B₂C at low temperatures.     

Oxygen nonstoichiometry and high temperature conductivity of the 2201 phase of the Bi---Sr---Cu---O superconducting oxide

The oxygen nonstoichiometry and high temperature conductivity of Bi_2.12Sr_1.86Cu_1.02O_y (2201 phase) were determined as a function of temperature (T) and oxygen partial pressure (P_O2). The dependences of conductivity on T and P_O2 were similar to those of oxygen content, and two subphases, and β, were found in such cases as 2212 and 2223 phases. From the result a close relationship was inferred between conductivity and oxygen content, and the mobility and carrier density were calculated. The carrier density of 2201 phase was smaller than those of the 2212 and 2223 phases.     

Anomalous magnetic behavior of the Co0.53Ga0.47 spin glass above the freezing temperature

We present here the detailed analysis of the magnetic behavior of the Co_0.53Ga_0.47 alloy, especially at temperatures above the freezing temperature T_f = 10 K. Low field static magnetization measurements were performed by using the SQUID magnetometer in the temperature range 5–65 K and magnetic fields up to 100 Oe. The temperature dependence of the field cooled susceptibility π_FC(T) at T > T_f has an anomaly, which is displayed in the double change of the curvature near T_s = 24 K. The data of magnetization M_FC in an external field H lie on a universal curve M_FC(H/T) at temperatures T_f < T < T_s. The plots of π^-1_FC(T) and non-linear magnetic susceptibility π^nl_FC(T^-3) are linear lines in the temperature range T_f−T_s. The strong deviation of π^-1_FC(T) and π^nl_FC(T^-3) from straight line, taking place at T T_s, indicates that T_s is an upper temperature limit of the classical superparamagnetic behavior with the constant cluster moment. The results suggest that such phenomena may be fairly universal for spin glasses.     

Density and bond-orientational relaxations in supercooled water

ABSTRACT

Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.     

Temperature reversibility of the remanent magnetization in powders of Y---Ba---Cu---O

The temperature dependence of the remanent magnetization M_R has been studied in YBa₂Cu₃O_6.9 powders cooled in a magnetic field. When the samples are heated up and cooled down again, M_R(T) is found to exhibit a reversible part when the density of vortices is initially low. For particle size comparable with the London penetration depth λ the reversible part of M_R(T) can be well described by λ(T).     

Critical behavior of transverse and longitudinal ac susceptibilities in a random anisotropy magnet a-Dy16Fe84

We have investigated critical lines in the H-T plane in a random anisotropy magnet (RAM) a-Dy₁₆Fe₈₄ with a small effective ratio of the anisotropy (D) to the exchange constant (J) by means of ac susceptibility (χ) in static fields H parallel and perpendicular to the ac field. We found that the transverse χ exhibits an anomaly along the irreversible line H(T_f) determined by previous magnetization measurements, while the longitudinal χ does so along a characteristic line H(T_i) in a lower temperature region. Above H(T_f) we also found an extra characteristic line H(T_c). The lines were almost independent of the measured frequency. Both the present results and previous magnetization results suggest that an equilibrium phase transition occurs, and the critical lines analogous to those in Heisenberg spin glasses are present in a weak RAM.     

Temperature and pressure dependence of NMR frequencies in ferromagnetic Heusler alloys containing cobalt and manganese

The ⁵⁹Co and ⁵⁵Mn NMR frequencies ν in Co₂MnZ (Z = Si, Ge, Sn and Ga) were measured as a function of temperature T and pressure P by the cw method. The ν/ν_4.2 value decreased faster for ⁵⁹Co than for ⁵⁵Mn with increasing T/T_C especially in Co₂MnGa, for which ∂ν/∂P was positive at 0°C in contrast to the results in other alloys.     

Double peak behavior of resistivity curves in Cd doped LaMnO3 perovskite systems

The effect of Cd doping on transport, magnetotransport, and magnetic properties has been investigated in the perovskite La_1−xCd_xMnO₃ (0x0.5) systems. The ρ(T) curves exhibit a sharp metal insulator transition (T_p1), which is close to paramagnetic to ferromagnetic transition (T_c) obtained from M−T curves for all samples. In addition, ρ(T) curves for Cd doped samples exhibit another broad transition (T_P2) below T_p1. This transition becomes more prominent and the transition temperature (T_p2) shifts to lower temperature with increasing Cd content. Such double peak behavior in the ρ(T) curve is attributed to the phase separation between the ferromagnetic metallic phases and the ferromagnetic insulating phases induced by the electronic inhomogeneity in the samples.     

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.     

Magnetic behaviour of some Mn.III2.VI4 compounds and their alloys

Measurement of the magnetic susceptibility χ as a function of temperature were made on polycrystalline samples from the alloy systems Cd_1−zMn_zGa₂Se₄, Zn_1−zMn_zGa₂Se₄ and Cd_1−zMn_zIn₂Te₄ which had been subjected to various heat treatments. The 1/χ versus T curves indicated that for the Zn---Se alloys, for all values of z, samples slowly cooled to room temperature were antiferromagnetic showing ideal Curie-Weiss behaviour, but for samples quenched from 700°C the behaviour was a mixture of antiferromagnetic and spin-glass. For the Cd---Se alloys, samples from the range (0.6 < z < 1.0) showed very similar behaviour, but in the range (0 < z < 0.6) even the very slowly cooled samples showed a mixture of antiferromagnetic and spin-glass behaviour. For the Cd---Te alloys, all samples, however heat-treated, showed spin-glass form. Values of the Curie-Weiss constant Ф were determined from all of the 1/χ versus T curves, and by comparison with the T(z) phase diagrams for the different alloy systems, the values of Ф were correlated with the ordering of the Mn atoms on the cation lattice. It is shown that the experimental values of Ф can give a very convenient way of determining the type of ordering and the degree of order in such alloys.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Spin hedgehog and collective magnetic quadrupole moments induced by parity and time invariance violating interaction

P- and T-odd interaction produces a spin distribution with the spins directed along the radius in spherically symmetric quantum systems. Due to the spin-dependent strong interaction this spin hedgehog contributes to P- and T-odd effects in neutron scattering, nuclear moments, etc. In deformed nuclei the P- and T-odd interaction produces a collective magnetic quadrupole moment. This moment induces P- and T -violating effects in atoms and molecules.     

ESR of double-perovskite Sr2FeMoO6

We present an ESR study of Sr₂FeMoO₆ in the paramagnetic region. A single line at g≈2 was associated with Fe³⁺ ions. The intensity follows Curie–Weiss law in the whole T range. For T >500 K a secondary line is attributed to ferromagnetic (FM) impurities. The line width is described by ΔH_pp(T)=ΔH_pp(∞)(1−Θ/T) with a high value for ΔH_pp(∞). The absence of narrowing effects is a signature of double-exchange (DE) interactions and indicates that DE drives the FM ordering at a relatively high T_c.     

Thermal transport properties in a He---He mixture near and below the superfluid transition

Measurements of the thermal conductivity and of X/T are reported for a ³He---⁴He mixture with a ³He mole fraction X = 0.622. At T_λ, X/T passes through a sharp peak. A comparison with the theory of Khalatnikov is presented. The relaxation times τ(T) to reach steady state conditions show qualitatively the same behaviors as X/T.