Quench Rate Research Articles

Effects of quenching on bending strength and piezoelectric properties of (Bi0.5Na0.5)TiO3 ceramics

ABSTRACT Lead-free piezoelectric bismuth sodium titanate (Bi0.5Na0.5)TiO3 (BNT) ceramics were prepared by quenching and the correlation among a depolarization temperature T d, the mechanical strength, and their piezoelectric properties were investigated. We controlled the quenching rate in the temperature range from 1100°C to 800°C. We examined the 5 patterns of the quenching rate (QR): 0.05 (ordinary firing, OF), 3.85, 5.77, 6.67, and 15.0 (quenching) oC/s. T d of the rapid quenched sample reached 229°C (QR = 15.0), but its mechanical strength decreased to a quarter of that of the OF ceramics. On the other hand, T d was 211°C at QR = 3.85 which was higher than that of OF-ceramic (QR = 0.05) at about 180°C. Moreover, three-point bending strength (227 MPa) of the quenched BNLT4 (QR = 3.85) was equivalent to that of the OF ceramics (235 MPa). Therefore, both T d and the mechanical strength were improved by controlling the quenching rate.

The role of quench rate on the plastic flow and fracture of three aluminium alloys with different grain structure and texture

The yielding, plastic flow and fracture of age hardenable aluminium alloys depend on the quench rate to room temperature after the solution heat-treatment at elevated temperature and before the artificial ageing. We investigate three AlMgSi alloys with different grain structure and crystallographic texture experimentally to determine the effects of quench rate (either water-quenching or air-cooling) on the precipitate microstructure and the mechanical properties, i.e., yield stress, work hardening and ductility. Tensile tests on smooth and V-notch specimens and Kahn tear tests are performed to study the influence of stress state on plastic flow and fracture. In addition, finite element simulations of the mechanical tests are performed for one of the alloys to investigate the validity of an extension of the Gurson model to high-exponent anisotropic plasticity. Transmission electron microscopy investigations show that the alloys and their precipitation microstructure are differently affected by the quench rate. Common for the three alloys is that the precipitate free zones around dispersoids and grain boundaries become larger, and the yield strength of the alloys becomes lower, after air-cooling than after water-quenching. The nanostructure model NaMo was modified to account for precipitate free zones, and was able to predict both the precipitation parameters and the tensile yield strength of all tempers and materials with a reasonable degree of accuracy, except in one case. In this case, the inhomogeneous precipitation in the material is too complex to be captured by the inherent precipitation model in NaMo. Due to the lower yield strength and higher work-hardening rate after air-cooling, the failure strain is increased for the smooth and V-notch tensile tests. The crack propagation energy, calculated from the Kahn tear tests, is markedly affected by the quench rate and the effect is different depending on the grain structure and plastic anisotropy, caused by the crystallographic texture. The anisotropic porous plasticity model used in the finite element simulations is able to precisely capture the fracture initiation in all the specimen geometries of the considered alloy, whereas the crack propagation energies of the Kahn tear tests are slightly overestimated.

Unconventional high-pressure Raman spectroscopy study of kinetic and peak pressure effects in plagioclase feldspars

We present the results of a high-pressure semi-hydrostatic study of two plagioclase minerals, andesine and albite, using diamond anvil cells (DACs) to characterize in situ variations in Raman spectra under different static pressures. In this work, we also examined the kinetic effects on deformation at both long and short timescales through non-traditional experiments in which the DAC was either dropped or struck with a mallet. We examined the effects of strain rate, quench rate, and pressure duration on the Raman spectra of plagioclase. We observed that amorphization occurred in all the plagioclase samples we analyzed, and that amorphization onset and permanence differ depending on the composition, kinetics, energy input, and peak pressure. In andesine, samples pressurized above a peak pressure of 18 GPa, amorphization is permanent. Below this critical pressure, the phase has ‘memory’, and crystalline andesine reforms on decompression. Our findings suggest the presence of a thermodynamic energy well in andesine around 18 GPa, and we show that any additional energy input while close to 18 GPa results in amorphization becoming permanent. The effect of the energy well may be relevant for longer duration impacts. For such impacts, equilibrium state studies of deformation and phase formation were previously considered to be applicable. These experiments illuminating the presence of memory effects in plagioclase have implications for comparing static compression, in which samples are measured while under compression, with shock compression, for which samples are measured after decompression.

Laser processing as a high-throughput method to investigate microstructure-processing-property relationships in multiprincipal element alloys

A direct laser deposition processing method was applied to construct compositional and microstructural libraries of AlxCoCrFeNi in an efficient and high-throughput manner. Among the compositions (x = 0.51–1.25) and quench rates (26–6400 K/s) studied, most of the laser deposited alloys exhibit a cellular microstructure, similar to the cast materials. The microstructural feature sizes were found to follow a power law relationship with the quench rate. The dependence of the microhardness on microstructural length scale was also investigated and observed to follow a Hall-Petch relationship. This study indicates that laser processing is an effective method for rapidly and efficiently evaluating multiprincipal element alloys and their microstructures.

Quench dynamics of Rydberg-dressed bosons on two-dimensional square lattices

We study the dynamics of bosonic atoms on a two-dimensional square lattice, where atomic interactions are long-ranged with either a box or soft-core shape. The latter can be realized through laser dressing ground-state atoms to electronically excited Rydberg states. When the range of interactions is equal or larger than the lattice constant, the system is governed by an extended Bose-Hubbard model. We propose a quench process by varying the atomic hopping linearly across phase boundaries of the Mott insulator-supersolid and supersolid-superfluid phases. Starting from a Mott insulating state, the dynamical evolution of the superfluid order parameter exhibits a universal behaviour at the early stage, largely independent of interactions. The dynamical evolution is significantly altered by strong, long-range interactions at later times. Particularly, we demonstrate that density wave excitation is important when the quench rate is small. Moreover, we show that the quench dynamics can be analyzed through time-of-flight images, i.e., measuring the momentum distribution and noise correlations.

Effects of melt spinning parameters on polypropylene hollow fiber formation

The objective of this research was to explore the effects of processing conditions on hollow fiber spinning, specifically to look at how differences in solidification impact hollow and solid fiber structures. Polypropylene hollow fibers were melt-spun with a four-segmented arc (4C) die under the wide ranges of spinning conditions (0.25–0.83 g/min of polymer mass throughput per a fiber, 500–2000 m/min of spinning speed, and 5%–100% quench rate). Fiber structure was explored through thermal, geometric, and tensile properties. Fiber hollowness depends on all spinning parameters studied (mass throughput, spinning speed, and quench rate). Increasing the quench rate resulted in the fiber solidifications closer to the spinneret. This leads to higher hollowness but also affected fiber tensile properties. When hollow and solid fibers were compared at constant quench, the hollow fiber solidified faster than solid fiber. The crystallinity of the fibers remained similar, but the tensile modulus was higher for hollow fiber than for solid fiber.

Influence of quench rate on multi-stage ageing of AA6014 alloy

The influence of quench rate after solution heat treatment on the microstructure in the as-quenched state and subsequent ageing kinetics of alloy AA6014 was investigated by means of transmission electron microscopy, positron annihilation lifetime spectroscopy and hardness measurements. Various ageing temperatures and stages were taken into consideration. Consistent with previous studies, we found that solute and vacancy supersaturation decrease during slow quenching due to precipitation and annihilation, respectively. Additionally, we observed cluster formation during cooling below 200 °C. As for the influence on ageing behaviour we observe different behaviour for high and low ageing temperature: Artificial ageing is more affected than pre-ageing and natural secondary ageing. The detrimental effect of natural ageing on paint-bake hardening also depends on the quench rate. Possible interpretations are associated with cluster formation during natural ageing and also during quenching. The influence of pre-ageing at different temperatures on subsequent ageing kinetics is similar for slower industrial-type quenching and for fast quenching, thus allowing to apply the findings from idealised quenching conditions to situations closer to real application.

On the glass forming ability (GFA), crystallization behavior and soft magnetic properties of nanomet-substituted alloys

This study was aimed to investigate the effect of substitution of Fe with Co, C, and Mo on the glass forming ability (GFA), crystallization behavior, and magnetic properties of Fe–B–Si–P–Cu (Nanomet) alloy. The thermodynamic parameters, PHS and PHSS, were used to guide towards increased GFA. The PHSS enhanced from −2.04 kJ/mol for Nanomet to −4.83 kJ/mol for a Co4C1Mo1 (at.%) substituted alloy. As a result, the critical quench rate reduced significantly, manifested as a drop of the required rotational speed from 3000 rpm to 2000 rpm. The temperature interval between two crystallization peaks enlarged for the substituted alloy, allowing a broader annealing range for nanocrystallization. The saturation magnetization (MS) and the coercivity (HC) were nearly maintained. This work confirms the relevance of the parameters PHS and PHSS to improve the GFA of the Nanomet alloy, and it is suggested that the same strategy can be applied for other alloys.

Universal dynamical scaling of long-range topological superconductors

We study the out-of-equilibrium dynamics of $p$-wave superconducting quantum wires with long-range interactions, when the chemical potential is linearly ramped across the topological phase transition. We show that the heat produced after the quench scales with the quench rate $\delta$ according to the scaling law $\delta^\theta$, where the exponent $\theta$ depends on the power law exponent of the long-range interactions. We identify the parameter regimes where this scaling can be cast in terms of the universal equilibrium critical exponents and can thus be understood within the Kibble-Zurek framework. When the electron hopping decays more slowly in space than pairing, it dominates the equilibrium scaling. Surprisingly, in this regime the dynamical critical behaviour arises only from paring and, thus, exhibits anomalous dynamical universality unrelated to equilibrium scaling. The discrepancy from the expected Kibble-Zurek scenario can be traced back to the presence of multiple universal terms in the equilibrium scaling functions of long-range interacting systems close to a second order critical point.

Effects of the Quenching Rate on the Microstructure, Mechanical Properties and Paint Bake-Hardening Response of Al–Mg–Si Automotive Sheets

The quenching rate of Al–Mg–Si alloys during solution treatment is an important parameter for the automotive industry. In this work, the effect of the different quenching rates on the microstructures, mechanical properties, and paint bake-hardening response of Al–Mg–Si sheets was studied. Large dimples form on the fracture surface of a sample at a quenching rate of 0.01 °C/s. When the quenching rate increased to 58.9 °C/s, the dimples became smaller. The recrystallized grains and textures were slightly affected by quenching rates beyond 1.9 °C/s. Thus, higher r values of the samples were achieved with slower quenching rates. Furthermore, only the Al(FeMn)SiCr insoluble phases were observed in samples with a rapid quenching rate. Sufficient solute atoms and vacancies resulted in the improvement of the precipitation kinetics and paint bake-hardening capacity for Al–Mg–Si sheets at rapid rates. With a decrease in the quenching rate, the formation of the rod-like coarse β′ phases consumed many solute atoms and vacancies, leading to the deterioration of the paint bake-hardening capacity. This study provides a critical reference on quenching rates for industrial practices, so that good mechanical properties can be achieved using precision control of the quenching process.

Dynamics of dissipative topological defects in coupled phase oscillators

The dynamics of topological defects in a system of coupled phase oscillators, arranged in one and two-dimensional arrays, was numerically investigated using the Kuramoto model. After a rapid decay of the number of topological defects, a long-time quasi steady state with few topological defects was detected. Two competing time scales governed the dynamics corresponding to the dissipation rate and the coupling quench rate. The density of topological defects scales as a power law function of the coupling quench rate ρ ∼ Cν with ν = 0.25. Reducing the number of topological defects improves the long time coherence and order parameter of the system, enhancing the probability to reach a global minimal loss state that can be mapped to the ground state of a classical XY spin Hamiltonian.

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

We analyze the quantum phase transitions taking place in a one-dimensional transverse field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in non-equilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferro- and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a non-equilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here it is found that the predicted non-equilibrium universal behavior, i.e. the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.

Kibble–Zurek universality in a strongly interacting Fermi superfluid

Near a continuous phase transition, systems with different microscopic origins display universal dynamics if their underlying symmetries are compatible. In a thermally quenched system, the Kibble-Zurek mechanism for the creation of topological defects unveils this universality through a characteristic power-law exponent, which captures the dependence of the defect density on the quench rate. Here, we report the observation of the Kibble-Zurek universality in a strongly interacting Fermi superfluid. As the system's microscopic description is tuned from bosonic to fermionic, the quench formation of vortices reveals a constant scaling exponent arising from the $U(1)$ gauge symmetry of the system. For rapid quenches, destructive vortex collisions lead to the saturation of their densities, whose values can be universally scaled by the interaction-dependent area of the vortex cores.

Quantum quench in non-relativistic fermionic field theory: harmonic traps and 2d string theory

We investigate a class of exactly solvable quantum quench protocols with a finite quench rate in systems of one dimensional non-relativistic fermions in external harmonic oscillator or inverted harmonic oscillator potentials, with time dependent masses and frequencies. These hamiltonians arise, respectively, in harmonic traps, and the c = 1 Matrix Model description of two dimensional string theory with time dependent string coupling. We show how the dynamics is determined by a single function of time which satisfies a generalized Ermakov-Pinney equation. The quench protocols we consider asymptote to constant masses and frequencies at early times, and cross or approach a gapless potential. In a right side up harmonic oscillator potential we determine the scaling behavior of the one point function and the entanglement entropy of a subregion by obtaining analytic approximations to the exact answers. The results are consistent with Kibble-Zurek scaling for slow quenches and with perturbation calculations for fast quenches. For cis-critical quench protocols the entanglement entropy oscillates at late times around its initial value. For end-critical protocols the entanglement entropy monotonically goes to zero inversely with time, reflecting the spread of fermions over the entire line. For the inverted harmonic oscillator potential, the dual collective field description is a scalar field in a time dependent metric and dilaton background.

Beyond the Horizon: Magneto-Optical Imaging Studies of the Kibble–Zurek Scenario in Superconductors

The Kibble–Zurek (Kibble in J Phys A 9:1387–1398, 1976; Zurek in Nature 317:505–508, 1985) scenario predicts that the outcome of a second-order phase transition from a disordered system into an ordered one depends on the quench rate. The emerging order parameter in the ordered state is not spatially uniform, containing topological defects. The faster the transition, the larger the density of defects. In the case of a conductor–superconductor transition, these defects are flux quanta (vortices). To investigate this scenario, we developed a high-resolution magneto-optical imaging system capable of resolving single flux quanta. Using this system, we imaged arrays of spontaneously created vortices in a Nb film. These vortices were formed after the film was rapidly cooled into the superconducting state at rates around 109 K/s. The internal correlations within the vortex array are important in order to differentiate between competing models. In the Kibble–Zurek scenario, neighboring vortices should have a different polarity, while in Hindmarsh–Rajantie (Hindmarsh and Rajantie in Phys Rev Lett 85:4660–4663, 2000) model the polarity should be the same. Our results favor the Kibble–Zurek scenario.

A vacancy‐rich, partially inverted spinelloid silicate, (Mg,Fe,Si)2(Si,□)O4, as a major matrix phase in shock melt veins of the Tenham and Suizhou L6 chondrites

AbstractA new high‐pressure silicate, (Mg,Fe,Si)2(Si,□)O4 with a tetragonal spinelloid structure, was discovered within shock melt veins in the Tenham and Suizhou meteorites, two highly shocked L6 ordinary chondrites. Relative to ringwoodite, this phase exhibits an inversion of Si coupled with intrinsic vacancies and a consequent reduction of symmetry. Most notably, the spinelloid makes up about 30–40 vol% of the matrix of shock veins with the remainder composed of a vitrified (Mg,Fe)SiO3 phase (in Tenham) or (Mg,Fe)SiO3‐rich clinopyroxene (in Suizhou); these phase assemblages constitute the bulk of the matrix in the shock veins. Previous assessments of the melt matrices concluded that majorite and akimotoite were the major phases. Our contrasting result requires revision of inferred conditions during shock melt cooling of the Tenham and Suizhou meteorites, revealing in particular a much higher quench rate (at least 5 × 103 K s−1) for veins of 100–500 μm diameter, thus overriding formation of the stable phase assemblage majoritic garnet plus periclase.

The quench control of water estimates in convergent margin magmas

AbstractHere we present a study on the quenchability of hydrous mafic melts. We show via hydrothermal experiments that the ability to quench a mafic hydrous melt to a homogeneous glass at cooling rates relevant to natural samples has a limit of no more than 9 ± 1 wt% of dissolved H2O in the melt. We performed supra-liquidus experiments on a mafic starting composition at 1–1.5 GPa spanning H2O-undersaturated to H2O-saturated conditions (from ~1 to ~21 wt%). After dissolving H2O and equilibrating, the hydrous mafic melt experiments were quenched. Quenching rates of 20 to 90 K/s at the glass transition temperature were achieved, and some experiments were allowed to decompress from thermal contraction while others were held at an isobaric condition during quench. We found that quenching of a hydrous melt to a homogeneous glass at quench rates comparable to natural conditions is possible at water contents up to 6 wt%. Melts containing 6–9 wt% of H2O are partially quenched to a glass, and always contain significant fractions of quench crystals and glass alteration/devitrification products. Experiments with water contents greater than 9 wt% have no optically clear glass after quench and result in fine-grained mixtures of alteration/devitrification products (minerals and amorphous materials). Our limit of 9 ± 1 wt% agrees well with the maximum of dissolved H2O contents found in natural glassy melt inclusions (8.5 wt% H2O). Other techniques for estimating pre-eruptive dissolved H2O content using petrologic and geochemical modeling have been used to argue that some arc magmas are as hydrous as 16 wt% H2O. Thus, our results raise the question of whether the observed record of glassy melt inclusions has an upper limit that is partially controlled by the quenching process. This potentially leads to underestimating the maximum amount of H2O recycled at arcs when results from glassy melt inclusions are predominantly used to estimate water fluxes from the mantle.

Complexity and scaling in quantum quench in 1 + 1 dimensional fermionic field theories

We consider the scaling behavior of circuit complexity under quantum quench in an a relativistic fermion field theory on a one dimensional spatial lattice. This is done by finding an exactly solvable quench protocol which asymptotes to massive phases at early and late times and crosses a critical point in between. We find a variety of scaling behavior as a function of the quench rate, starting with a saturation for quenches at the lattice scale, a “fast quench scaling” at intermediate rate and a Kibble Zurek scaling at slow rates.

Shear-Transformation Zone Activation during Loading and Unloading in Nanoindentation of Metallic Glasses

Using molecular dynamics simulation, we study nanoindentation in large samples of Cu–Zr glass at various temperatures between zero and the glass transition temperature. We find that besides the elastic modulus, the yielding point also strongly (by around 50%) decreases with increasing temperature; this behavior is in qualitative agreement with predictions of the cooperative shear model. Shear-transformation zones (STZs) show up in increasing sizes at low temperatures, leading to shear-band activity. Cluster analysis of the STZs exhibits a power-law behavior in the statistics of STZ sizes. We find strong plastic activity also during the unloading phase; it shows up both in the deactivation of previous plastic zones and the appearance of new zones, leading to the observation of pop-outs. The statistics of STZs occurring during unloading show that they operate in a similar nature as the STZs found during loading. For both cases, loading and unloading, we find the statistics of STZs to be related to directed percolation. Material hardness shows a weak strain-rate dependence, confirming previously reported experimental findings; the number of pop-ins is reduced at slower indentation rate. Analysis of the dependence of our simulation results on the quench rate applied during preparation of the glass shows only a minor effect on the properties of STZs.

Entanglement spreading and oscillation

We study dynamics of quantum entanglement in smooth global quenches with a finite rate, by computing the time evolution of entanglement entropy in 1 + 1 dimensional free scalar theory with time-dependent masses which start from a nonzero value at early time and either crosses or approaches zero. The time-dependence is chosen so that the quantum dynamics is exactly solvable. If the quenches asymptotically approach a critical point at late time, the early-time and late-time entropies are proportional to the time and subsystem size respectively. Their proportionality coefficients are determined by scales: in a fast limit, an initial correlation length; in a slow limit, an effective scale defined when adiabaticity breaks down. If the quenches cross a critical point, the time evolution of entropy is characterized by the scales: the initial correlation length in the fast limit and the effective correlation length in the slow limit. The entropy oscillates, and the entanglement oscillation comes from a coherence between right-moving and left-moving waves if we measure the entropy after time characterized by the quench rate. The periodicity of the late-time oscillation is consistent with the periodicity of the oscillation of zero modes which are zero-momentum value of two point functions of a fundamental field and its conjugate momentum.