Microscopic Relaxation Time Research Articles

Intrinsic relaxation in a supercooled ZrTiNiCuBe glass forming liquid

We studied structural relaxation in the bulk metallic glass forming alloy ${\mathrm{Zr}}_{46.8}{\mathrm{Ti}}_{8.2}{\mathrm{Cu}}_{7.5}{\mathrm{Ni}}_{10}{\mathrm{Be}}_{27.5}$ on different timescales and length scales, with emphasis on the supercooled liquid state. Using x-ray photon correlation spectroscopy, we determined the microscopic structural relaxation time covering timescales of more than two decades in the supercooled liquid region, down to the subsecond regime. Upon heating across the glass transition, the intermediate scattering function changes from a compressed to a stretched decay, with a smooth transition in the stretching exponent and characteristic relaxation time. In the supercooled liquid state, the macroscopic and microscopic relaxation time and the melt viscosity all exhibit the same temperature dependence. This points to a relaxation mechanism via intrinsic structural relaxation of the majority component Zr, with its microscopic timescale controlling both the stress relaxation and viscous flow of the melt.

Continuous random network avoidance and microscopic relaxation time in As2Se3 glass

Recent nuclear magnetic resonance (NMR) studies on SiO2 structural glass has shown a positive correlation exists between Si-O bond lengths and Si-O-Si bond angles. This indicates that when the glass solidified it avoided forming as a continuous random network (CRN). A microscopic tight binding (TB) model was used some years ago to predict the nuclear quadrupole resonance (NQR) distribution of powdered As2Se3 glass. Similar bond length- bond angle correlations were found. Here we extend this model and show that these correlations are directly attributable to a competition between valence electronic energy and emergent frustration forces as the glass solidifies into a locally preferred structure (LPS). Recent studies have shown that fast atomic motion occurs in metallic glasses at temperatures far below the glass temperature. Using this model we calculate a microscopic relaxation time and show it is a product of CRN avoidance.

Antiferromagnetism, spin-glass state, H–T phase diagram, and inverse magnetocaloric effect in Co2RuO4

Static and dynamic magnetic properties of normal spinel Co2RuO4 = (Co2+) are reported based on our investigations of the temperature (T), magnetic field (H) and frequency (f) dependence of the ac-magnetic susceptibilities and dc-magnetization (M) covering the temperature range T = 2 K–400 K and H up to 90 kOe. These investigations show that Co2RuO4 exhibits an antiferromagnetic (AFM) transition at TN ∼ 15.2 K, along with a spin-glass state at slightly lower temperature (TSG) near 14.2 K. It is argued that TN is mainly governed by the ordering of the spins of Co2+ ions occupying the A-site, whereas the exchange interaction between the Co2+ ions on the A-site and randomly distributed Ru3+ on the B-site triggers the spin-glass phase, Co3+ ions on the B-site being in the low-spin non-magnetic state. Analysis of measurements of M (H, T) for T < TN are used to construct the H–T phase diagram showing that TSG shifts to lower T varying as H2/3.2 expected for spin-glass state whereas TN is nearly H-independent. For T > TN, analysis of the paramagnetic susceptibility (χ) vs. T data are fit to the modified Curie–Weiss law, χ = χ0 + C/(T + θ), with χ0 = 0.0015 emu mol−1Oe−1 yielding θ = 53 K and C = 2.16 emu-K mol−1Oe−1, the later yielding an effective magnetic moment μeff = 4.16 μB comparable to the expected value of μeff = 4.24 μB per Co2RuO4. Using TN, θ and high temperature series for χ, dominant exchange constant J1/kB ∼ 6 K between the Co2+ on the A-sites is estimated. Analysis of the ac magnetic susceptibilities near TSG yields the dynamical critical exponent zν = 5.2 and microscopic spin relaxation time τ0 ∼ 1.16 × 10−10 sec characteristic of cluster spin-glasses and the observed time-dependence of M(t) is supportive of the spin-glass state. Large M–H loop asymmetry at low temperatures with giant exchange bias effect (HEB ∼ 1.8 kOe) and coercivity (HC ∼ 7 kOe) for a field cooled sample further support the mixed magnetic phase nature of this interesting spinel. The negative magnetocaloric effect observed below TN is interpreted to be due to the AFM and SG ordering. It is argued that the observed change from positive MCE (magnetocaloric effect) for T > TN to inverse MCE for T < TN observed in Co2RuO4 (and reported previously in other systems also) is related to the change in sign of (∂M/∂T) vs. T data.

Thickness-dependent electron momentum relaxation times in iron films

Terahertz time-domain conductivity measurements in 2–100 nm thick iron films resolve the femtosecond time delay between the applied electric fields and the resulting currents. This current response time decreases from 29 fs for the thickest films to 7 fs for the thinnest films. The macroscopic response time is not strictly proportional to the conductivity. This excludes the existence of a single relaxation time universal for all conduction electrons. We must assume a distribution of microscopic momentum relaxation times. The macroscopic response time depends on the average and variation of this distribution; the observed deviation between the response time and conductivity scaling corresponds to the scaling of the variation. The variation of microscopic relaxation times depends on the film thickness because electrons with different relaxation times are affected differently by the confinement since they have different mean free paths.

Role of many-body correlation in slow dynamics of glass-forming liquids: intrinsic or perturbative

Upon cooling or densification, a supercooled liquid shows drastic slowing down toward its glass-transition point. The physical mechanism behind this slow glassy dynamics has been a matter of discussion for a long time, but there has still been no consensus on its origin. Recently, we have found that for systems mainly interacting with steric repulsions, glassy structural order (or, angular order) generally develops upon cooling and its correlation length, , grows as ( is the bare correlation length, T is the temperature, T0 is the hypothetical ideal glass transition, and d is the spatial dimensionality). This ordering is difficult to detect by two-body density correlation since it is a consequence of sterically-induced (entropically-driven) many-body correlation that lowers local free energy. Interestingly, the power-law growth of with the exponent of 2/d is reminiscent of the Ising criticality. We also find that the structural relaxation time diverges as (: the microscopic relaxation time, K is a fragility index, is the Boltzmann constant), suggesting that glass transition is a consequence of Ising-like criticality with growing activation energy. Unlike ordinary critical phenomena, the activation energy of particle motion increases in proportion to the root of the correlation volume of , implying that the particle motion is strongly correlated in that volume. This relation indicates that the impact of spatial fluctuations of the order parameter on slow dynamics is not perturbative but intrinsic. Although we need further study to confirm our claim, we hope that the discussion in this article would provide a good starting point for further consideration of the physical nature of glass transition.

Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid.

If a liquid is cooled rapidly to form a glass, its structural relaxation becomes retarded, producing a drastic increase in viscosity. In two dimensions, strong long-wavelength fluctuations persist, even at low temperature, making it difficult to evaluate the microscopic structural relaxation time. This Letter shows that, in a 2D glass-forming liquid, relative displacement between neighbor particles yields a relaxation time that grows in proportion to the viscosity. In addition to thermal elastic vibrations, hydrodynamic fluctuations are found to affect the long-wavelength dynamics, yielding a logarithmically diverging diffusivity in the long-time limit.

Transits of the QCD critical point

We analyze the evolution of hydrodynamic fluctuations in a heavy-ion collision as the system passes close to the QCD critical point. We introduce two small dimensionless parameters $\ensuremath{\lambda}$ and ${\mathrm{\ensuremath{\Delta}}}_{s}$ to characterize the evolution. $\ensuremath{\lambda}$ compares the microscopic relaxation time (away from the critical point) to the expansion rate $\ensuremath{\lambda}\ensuremath{\equiv}{\ensuremath{\tau}}_{0}/{\ensuremath{\tau}}_{Q}$, and ${\mathrm{\ensuremath{\Delta}}}_{s}$ compares the baryon to entropy ratio, $n/s$, to its critical value, ${\mathrm{\ensuremath{\Delta}}}_{s}\ensuremath{\equiv}(n/s\ensuremath{-}{n}_{c}/{s}_{c})/({n}_{c}/{s}_{c})$. We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on $\ensuremath{\lambda}$ and ${\mathrm{\ensuremath{\Delta}}}_{s}$. Finally, we use this parametric reasoning to estimate the critical fluctuations and correlation length for a heavy-ion collision and to give guidance to the experimental search for the QCD critical point.

Evolution of structure and dynamics of thermo-reversible nanoparticle gels-A combined XPCS and rheology study.

A combined X-ray photon correlation spectroscopy and rheology study is carried out to capture the evolution of structure, fast particle-scale dynamics, and moduli (elastic and loss) at early times of gel formation near the fluid-gel boundary of a suspension of nanoparticles. The system is comprised of moderately concentrated suspensions of octadecyl silica in decalin (ϕ = 0.2) undergoing thermoreversible gelation. Near the gel boundary, the rate of gel formation is very sensitive to changes in attraction strength. However, we find that at different attraction strengths, the system goes through identical intermediate states of microscopic and macroscopic behavior, even though the absolute time needed to form a gel varies by orders of magnitude. We identify a single dimensionless time parameter, tw/tg, where tw is the wait time following the quench and tg is the rheologically determined gel time, that captures the similarity in gel formation at a range of attraction strengths. Following a temperature quench below the gel boundary, the system is initially fluidlike and forms diffusive clusters (∼8.5 times the particle diameter). After a lag-time, tL, clusters aggregate to form a network like structure which is characterized by the onset of mechanical rigidity and a rapid growth in microscopic relaxation times. At tg, the Baxter parameter obtained from adhesive hard sphere fits of the structure factor attains a constant value corresponding to the theoretical percolation boundary, thus demonstrating that gelation is percolation driven.

Cationic distribution, exchange interactions, and relaxation dynamics in Zn-diluted MnCo2O4 nanostructures

We report an experimental investigation of the electronic structure and magnetic properties of bulk and nanosized MnCo2O4 diluted with Zn. The cationic distribution for tetrahedral A-site dilution is (Co1−yA2+ZnyA2+)A[Mn3+Co3+]BO4±δ, whereas B-site dilution results in (Co2+)A[Mn1−xB3+ZnxB2+Co3+]BO4−δ. The strength of exchange interaction Jij between the magnetic ions in a bulk spinel lattice decreases by ∼15% for A-site dilution relative to the undiluted compound; however, B-site dilution results in an enhancement in Jij by 17%. The frequency and temperature dependence of dynamic-susceptibility [χac(f,T)] studies of nanostructured compounds reveals the existence of spin-glass like behavior below the freezing temperature TF∼125.7K (for xB=0.2) and 154.3 K (yA=0.1). Relaxation time τ follows the Power-Law variation with a dynamical critical exponent zν=6.17 and microscopic spin relaxation time τo=4.4×10−15s for xB=0.2 (for yA=0.1, zν=5.2 and τo=5.4×10−13s). The amplitude and peak position in χac(T) decreases with an increase in the DC bias field, which indicates that the spin-glass phase can survive in the presence of low fields forming a critical line with an exponent 2/3. This behavior is similar to the de Almeida-Thouless (AT-line) analysis in the T-H phase diagram which supports the existence of spin-glass like behavior below TF in these Zn diluted spinels.

Common glass-forming spin-liquid state in the pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7

Despite a well-ordered pyrochlore crystal structure and strong magnetic interactions between the Dy$^{3+}$ or Ho$^{3+}$ ions, no long range magnetic order has been detected in the pyrochlore titanates Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$. To explore the actual magnetic phase formed by cooling these materials, we measure their magnetization dynamics using toroidal, boundary-free magnetization transport techniques. We find that the dynamical magnetic susceptibility of both compounds has the same distinctive phenomenology, that is indistinguishable in form from that of the dielectric permittivity of dipolar glass-forming liquids. Moreover, Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$ both exhibit microscopic magnetic relaxation times that increase along the super-Arrhenius trajectories analogous to those observed in glass-forming dipolar liquids. Thus, upon cooling below about 2K, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ both appear to enter the same magnetic state exhibiting the characteristics of a glass-forming spin-liquid.

Molecular mobility in driven monomeric and polymeric glasses.

We show that in monomeric supercooled liquids and glasses that are plastically flowing at a constant shear stress σ while being deformed with strain rate ε[over ̇], the microscopic structural relaxation time τ_{str} is given by the universal relation σ/G_{∞}ε[over ̇] with G_{∞} a modulus. This equality holds for all rheological regimes from temperatures above the glass transition all the way to the athermal limit, and arises from the competing effects of elastic loading and viscous dissipation. In macromolecular (polymeric) glasses, however, the stress decouples from this relaxation time and τ_{str} is in fact further reduced even though σ rises during glassy strain hardening. We develop expressions to capture both effects and thus provide a framework for analyzing mobility measurements in glassy materials.

Stokes-Einstein relation of the liquid metal rubidium and its relationship to changes in the microscopic dynamics with increasing temperature.

For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

Memory behaviors of entropy production rates in heat conduction

Based on the relaxation time approximation and first-order expansion, memory behaviors in heat conduction are found between the macroscopic and Boltzmann–Gibbs–Shannon (BGS) entropy production rates with exponentially decaying memory kernels. In the frameworks of classical irreversible thermodynamics (CIT) and BGS statistical mechanics, the memory dependency on the integrated history is unidirectional, while for the extended irreversible thermodynamics (EIT) and BGS entropy production rates, the memory dependences are bidirectional and coexist with the linear terms. When macroscopic and microscopic relaxation times satisfy a specific relationship, the entropic memory dependences will be eliminated. There also exist initial effects in entropic memory behaviors, which decay exponentially. The second-order term are also discussed, which can be understood as the global non-equilibrium degree. The effects of the second-order term are consisted of three parts: memory dependency, initial value and linear term. The corresponding memory kernels are still exponential and the initial effects of the global non-equilibrium degree also decay exponentially.

Sub-Tg relaxation times of the α process in metallic glasses

The current view of structural relaxation in metallic glasses assumes the presence of primary and secondary processes with different activation energies. While the faster, secondary process can be well characterized in the out-of-equilibrium state below the glass transition temperature Tg, the experimental direct determination of the primary process in this temperature region is more difficult due to the long relaxation times. In this work, we merge new and literature data to analyze the temperature behavior of the primary relaxation time below Tg as observed by mechanical spectroscopy and stress relaxation of metallic glasses of different fragility. We compare these results with the microscopic structural relaxation times previously measured with X-ray photon correlation spectroscopy. The coincidence between the macroscopic and microscopic relaxation times allows us to discuss the underlying mechanisms responsible of primary relaxation over different length scales, as well as to propose an overall picture of the primary relaxation behavior in the glassy regime near Tg.

Comparing the atomic and macroscopic aging dynamics in an amorphous and partially crystalline Zr44Ti11Ni10Cu10Be25bulk metallic glass

Abstract

Transient and oscillating response of Ovonic devices for high-speed electronics

The electric response of Ovonic devices to a time-dependent voltage is analysed by means of a charge-transport model previously proposed by the authors. The numerical implementation of the model shows that the features of the I(V) characteristics depend not only upon the external bias but also on more complex effects due to the interplay between intrinsic microscopic relaxation times and the inevitable parasitic elements of the system. Either stable or oscillating solutions are found, according to the position of the load line. The model also allows for speculation on the potential of Ovonic materials in the design of selector devices for two-terminal non-volatile memories.

GMI in the reentrant spin-glass Fe90Zr10 alloy: Investigation of the spin dynamics in the MHz frequency regime

Giant magnetoimpedance (GMI) in the reentrant spin-glass (SG) phase of ferromagnetic Fe90Zr10 is reported. The temperature (T) dependence of the GMI allows the investigation of the spin dynamics in the SG phase in the MHz frequency regime and thus very short relaxation times τ (∼10−8 s). The GMI shows a broad maximum around 150 K and diminishes with decreasing T below the glass temperature Tg of 15 K. The magnetic permeability data obtained from the GMI data show the general features observed in the ac magnetic susceptibility measured at lower frequencies (10 ≤ f ≤ 104 Hz), yielding values of Tf (=Tg(f)) that allow testing the validity of the power-law scaling used for describing the dynamics of SG-phases up to 15 MHz. A log-log plot of τ (=1/f) versus the reduced critical temperature shows two distinct regimes in the time-domain: (1) a critical slowing-down is observed for values τ &amp;gt; 3 × 10−3 s; and (2) for 7 × 10−8 ≤ τ ≤ 3 × 10−3 s. In the latter case a fitting to the power-law yields the value 7.4 for the product of the critical exponents zν, and 1.6 × 10−7 s for the microscopic relaxation time τ0. The product of the exponents is appropriate for an Ising spin glass.

Extended Hydrodynamic Models and Multigrid Solver of a Silicon Diode Simulation

AbstractExtended hydrodynamic models for carrier transport are derived from the semiconductor Boltzmann equation with relaxation time approximation of the scattering term, by using the globally hyperbolic moment method and the moment-dependent relaxation time. Incorporating the microscopic relaxation time and the applied voltage bias, a formula is proposed to determine the relaxation time for each moment equation, which sets different relaxation rates for different moments such that higher moments damp faster. The resulting models would give more satisfactory results of macroscopic quantities of interest with a high-order convergence to those of the underlying Boltzmann equation as the involved moments increase, in comparison to the corresponding moment models using a single relaxation time. In order to simulate the steady states efficiently, a multigrid solver is developed for the derived moment models. Numerical simulations of an n+-n-n+ silicon diode are carried out to demonstrate the validation of the presented moment models, and the robustness and efficiency of the designed multigrid solver.

Kinetics of the glass transition of fragile soft colloidal suspensions.

Microscopic relaxation time scales are estimated from the autocorrelation functions obtained by dynamic light scattering experiments for Laponite suspensions with different concentrations (CL), added salt concentrations (CS), and temperatures (T). It has been shown in an earlier work [D. Saha, Y. M. Joshi, and R. Bandyopadhyay, Soft Matter 10, 3292 (2014)] that the evolutions of relaxation time scales of colloidal glasses can be compared with molecular glass formers by mapping the waiting time (tw) of the former with the inverse of thermodynamic temperature (1/T) of the latter. In this work, the fragility parameter D, which signifies the deviation from Arrhenius behavior, is obtained from fits to the time evolutions of the structural relaxation time scales. For the Laponite suspensions studied in this work, D is seen to be independent of CL and CS but is weakly dependent on T. Interestingly, the behavior of D corroborates the behavior of fragility in molecular glass formers with respect to equivalent variables. Furthermore, the stretching exponent β, which quantifies the width w of the spectrum of structural relaxation time scales, is seen to depend on tw. A hypothetical Kauzmann time tk, analogous to the Kauzmann temperature for molecular glasses, is defined as the time scale at which w diverges. Corresponding to the Vogel temperature defined for molecular glasses, a hypothetical Vogel time tα (∞) is also defined as the time at which the structural relaxation time diverges. Interestingly, a correlation is observed between tk and tα (∞), which is remarkably similar to that known for fragile molecular glass formers. A coupling model that accounts for the tw-dependence of the stretching exponent is used to analyse and explain the observed correlation between tk and tα (∞).

Supercooled spin liquid state in the frustrated pyrochlore Dy2Ti2O7

A "supercooled" liquid develops when a fluid does not crystallize upon cooling below its ordering temperature. Instead, the microscopic relaxation times diverge so rapidly that, upon further cooling, equilibration eventually becomes impossible and glass formation occurs. Classic supercooled liquids exhibit specific identifiers including microscopic relaxation times diverging on a Vogel-Tammann-Fulcher (VTF) trajectory, a Havriliak-Negami (HN) form for the dielectric function ε(ω, T), and a general Kohlrausch-Williams-Watts (KWW) form for time-domain relaxation. Recently, the pyrochlore Dy2Ti2O7 has become of interest because its frustrated magnetic interactions may, in theory, lead to highly exotic magnetic fluids. However, its true magnetic state at low temperatures has proven very difficult to identify unambiguously. Here, we introduce high precision, boundary-free magnetization transport techniques based upon toroidal geometries and gain an improved understanding of the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7. We demonstrate a virtually universal HN form for the magnetic susceptibility χ (ω, T), a general KWW form for the realtime magnetic relaxation, and a divergence of the microscopic magnetic relaxation rates with the VTF trajectory. Low-temperature Dy2Ti2O7 therefore exhibits the characteristics of a supercooled magnetic liquid. One implication is that this translationally invariant lattice of strongly correlated spins may be evolving toward an unprecedented magnetic glass state, perhaps due to many-body localization of spin.